Quick Answer
SAT trigonometric ratios practice questions test sine, cosine, tangent, right-triangle side relationships, special angles, complementary angles, slopes, angles of elevation, and real-world models.
What Should You Know?
- sin θ=opposite/hypotenuse.
- cos θ=adjacent/hypotenuse.
- tan θ=opposite/adjacent.
- The hypotenuse is opposite the right angle.
- 45-45-90 ratio: 1:1:√2.
- 30-60-90 ratio: 1:√3:2.
- For an acute line angle, slope=tan θ.
- sin²θ+cos²θ=1.
In This Guide
Start With SAT Math Topic-Wise Practice
Connect trigonometry practice with weekly score planning and targeted SAT Math correction.
Download the SAT Prep Guide E-Book
Organize trigonometric ratios and right-triangle practice with a clear weekly plan.
Download SAT Prep Guide E-BookWhat Does the SAT Test in Trigonometric Ratio Questions?
Students may need to identify a ratio, find a missing side, use an exact value, interpret slope as tangent, or model a height, distance, ramp, or angle of elevation.
| Skill Area | What It Tests | Questions |
|---|---|---|
| Trig basics | SOH-CAH-TOA | Q1-Q15 |
| Finding sides | Right triangles and exact values | Q16-Q30 |
| Special angles | 30°, 45°, 60°, complements | Q31-Q45 |
| Applications | Slopes, elevations, mixed ratios | Q46-Q70 |
Download Free SAT Study Resources For U.S. Students
To begin your preparation with organized practice, download our free SAT Prep E-Book, SAT Math Question Bank, and SAT English Question Bank. These tools are intended to assist students in comprehending the style of the Digital SAT, increasing their accuracy, and boosting their self-assurance prior to test day.
How Are Sine, Cosine, and Tangent Basics Tested?
Identify opposite, adjacent, and hypotenuse sides and write the correct ratio.
TRIGONOMETRIC RATIO BASICSEASYQuestion 1
Which ratio represents sin θ?
Which choice is correct?
A) adjacent/hypotenuse
B) opposite/hypotenuse
C) opposite/adjacent
D) hypotenuse/opposite
Show full solution
Correct answer: B) opposite/hypotenuse
sin θ=opposite/hypotenuse.
SAT trap: Use SOH.
TRIGONOMETRIC RATIO BASICSEASYQuestion 2
Which ratio represents cos θ?
Which choice is correct?
A) adjacent/hypotenuse
B) opposite/hypotenuse
C) opposite/adjacent
D) hypotenuse/adjacent
Show full solution
Correct answer: A) adjacent/hypotenuse
cos θ=adjacent/hypotenuse.
SAT trap: Use CAH.
TRIGONOMETRIC RATIO BASICSEASYQuestion 3
Which ratio represents tan θ?
Which choice is correct?
A) adjacent/hypotenuse
B) opposite/hypotenuse
C) opposite/adjacent
D) hypotenuse/opposite
Show full solution
Correct answer: C) opposite/adjacent
tan θ=opposite/adjacent.
SAT trap: Use TOA.
TRIGONOMETRIC RATIO BASICSEASYQuestion 4
Opposite=6 and hypotenuse=10. What is sin θ?
Which choice is correct?
A) 3/5
B) 4/5
C) 5/3
D) 5/4
Show full solution
Correct answer: A) 3/5
6/10=3/5.
SAT trap: Reduce the fraction.
TRIGONOMETRIC RATIO BASICSEASYQuestion 5
Adjacent=8 and hypotenuse=17. What is cos θ?
Which choice is correct?
A) 8/15
B) 8/17
C) 15/17
D) 17/8
Show full solution
Correct answer: B) 8/17
cos θ=8/17.
SAT trap: Use adjacent over hypotenuse.
TRIGONOMETRIC RATIO BASICSEASYQuestion 6
Opposite=9 and adjacent=12. What is tan θ?
Which choice is correct?
A) 3/4
B) 4/3
C) 9/21
D) 12/21
Show full solution
Correct answer: A) 3/4
9/12=3/4.
SAT trap: Tangent does not use the hypotenuse.
TRIGONOMETRIC RATIO BASICSEASYQuestion 7
In a 3-4-5 triangle, θ is opposite the side 3. What is sin θ?
Which choice is correct?
A) 3/4
B) 3/5
C) 4/5
D) 5/3
Show full solution
Correct answer: B) 3/5
sin θ=3/5.
SAT trap: The hypotenuse is 5.
TRIGONOMETRIC RATIO BASICSEASYQuestion 8
In a 5-12-13 triangle, θ is adjacent to side 12. What is cos θ?
Which choice is correct?
A) 5/13
B) 12/13
C) 5/12
D) 13/12
Show full solution
Correct answer: B) 12/13
cos θ=12/13.
SAT trap: Identify the adjacent leg.
TRIGONOMETRIC RATIO BASICSEASYQuestion 9
In an 8-15-17 triangle, θ is opposite side 15. What is tan θ?
Which choice is correct?
A) 8/15
B) 15/8
C) 15/17
D) 8/17
Show full solution
Correct answer: B) 15/8
tan θ=15/8.
SAT trap: Use opposite over adjacent.
TRIGONOMETRIC RATIO BASICSEASYQuestion 10
If sin θ=5/13, which lengths can be opposite and hypotenuse?
Which choice is correct?
A) 5 and 12
B) 5 and 13
C) 12 and 13
D) 13 and 5
Show full solution
Correct answer: B) 5 and 13
Sine is opposite over hypotenuse.
SAT trap: The denominator is the hypotenuse.
TRIGONOMETRIC RATIO BASICSMEDIUMQuestion 11
If cos θ=7/25, which lengths can be adjacent and hypotenuse?
Which choice is correct?
A) 7 and 24
B) 24 and 25
C) 7 and 25
D) 25 and 7
Show full solution
Correct answer: C) 7 and 25
Cosine is adjacent over hypotenuse.
SAT trap: Keep the order correct.
TRIGONOMETRIC RATIO BASICSMEDIUMQuestion 12
If tan θ=4/7, which lengths can be opposite and adjacent?
Which choice is correct?
A) 4 and 7
B) 7 and 4
C) 4 and √65
D) 7 and √65
Show full solution
Correct answer: A) 4 and 7
Tangent is opposite over adjacent.
SAT trap: Do not reverse the ratio.
TRIGONOMETRIC RATIO BASICSMEDIUMQuestion 13
If sin θ=3/5 and cos θ=4/5, what is tan θ?
Which choice is correct?
A) 3/4
B) 4/3
C) 3/5
D) 4/5
Show full solution
Correct answer: A) 3/4
tan θ=(3/5)/(4/5)=3/4.
SAT trap: Use tan θ=sin θ/cos θ.
TRIGONOMETRIC RATIO BASICSMEDIUMQuestion 14
If sin θ=12/13 and θ is acute, what is cos θ?
Which choice is correct?
A) 5/13
B) 12/13
C) 13/12
D) √13/13
Show full solution
Correct answer: A) 5/13
Use the 5-12-13 triangle.
SAT trap: Find the missing leg.
TRIGONOMETRIC RATIO BASICSMEDIUMQuestion 15
If cos θ=15/17 and θ is acute, what is sin θ?
Which choice is correct?
A) 8/15
B) 8/17
C) 15/8
D) 17/8
Show full solution
Correct answer: B) 8/17
Use the 8-15-17 triangle.
SAT trap: Find the opposite leg.
Build Stronger SAT Trigonometry Skills
Connect SOH-CAH-TOA with special triangles and real SAT timing.
How Are Missing Sides Found With Trigonometry?
Use trigonometric ratios, special triangles, and proportions.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 16
sin 30°=x/10. What is x?
Which choice is correct?
A) 2
B) 5
C) 5√3
D) 10
Show full solution
Correct answer: B) 5
sin 30°=1/2, so x=5.
SAT trap: Use the exact value.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 17
cos 60°=x/18. What is x?
Which choice is correct?
A) 6
B) 9
C) 9√3
D) 18
Show full solution
Correct answer: B) 9
cos 60°=1/2, so x=9.
SAT trap: Cos 60° is 1/2.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 18
tan 45°=x/7. What is x?
Which choice is correct?
A) 1
B) 7
C) 7√2
D) 14
Show full solution
Correct answer: B) 7
tan 45°=1.
SAT trap: The legs are equal.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 19
A right triangle has hypotenuse 20 and angle 30°. Find the opposite side.
Which choice is correct?
A) 5
B) 10
C) 10√3
D) 20√3
Show full solution
Correct answer: B) 10
20 sin 30°=10.
SAT trap: The short leg is half the hypotenuse.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 20
A right triangle has hypotenuse 16 and angle 60°. Find the adjacent side.
Which choice is correct?
A) 8
B) 8√3
C) 16√3
D) 32
Show full solution
Correct answer: A) 8
16 cos 60°=8.
SAT trap: The adjacent side is the short leg.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 21
A right triangle has adjacent side 12 and angle 45°. Find the opposite side.
Which choice is correct?
A) 6
B) 12
C) 12√2
D) 24
Show full solution
Correct answer: B) 12
tan 45°=1, so opposite=12.
SAT trap: 45-45-90 legs are equal.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 22
A right triangle has opposite side 6 and angle 30°. Find the hypotenuse.
Which choice is correct?
A) 6√2
B) 6√3
C) 12
D) 18
Show full solution
Correct answer: C) 12
sin 30°=6/h=1/2.
SAT trap: Double the short leg.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 23
A right triangle has adjacent side 5√3 and angle 30°. Find the opposite side.
Which choice is correct?
A) 5
B) 5√2
C) 10
D) 15
Show full solution
Correct answer: A) 5
Use the 1:√3:2 ratio.
SAT trap: Adjacent to 30° is the long leg.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 24
A 10-foot ladder makes a 60° angle with the ground. How high does it reach?
Which choice is correct?
A) 5
B) 5√2
C) 5√3
D) 10√3
Show full solution
Correct answer: C) 5√3
Height=10 sin 60°=5√3.
SAT trap: The ladder is the hypotenuse.
FINDING SIDES WITH TRIGONOMETRYMEDIUMQuestion 25
A ramp rises 4 feet over a 12-foot run. What is tan θ?
Which choice is correct?
A) 1/4
B) 1/3
C) 3
D) 4
Show full solution
Correct answer: B) 1/3
tan θ=4/12=1/3.
SAT trap: Use rise over run.
FINDING SIDES WITH TRIGONOMETRYHARDQuestion 26
Opposite=7 and hypotenuse=25. Find the adjacent side.
Which choice is correct?
A) 18
B) 24
C) 25
D) 32
Show full solution
Correct answer: B) 24
√(25²-7²)=24.
SAT trap: Use the Pythagorean theorem.
FINDING SIDES WITH TRIGONOMETRYHARDQuestion 27
Adjacent=9 and hypotenuse=15. What is sin θ?
Which choice is correct?
A) 3/5
B) 4/5
C) 9/15
D) 15/9
Show full solution
Correct answer: B) 4/5
The opposite side is 12, so sin θ=12/15.
SAT trap: Find the missing leg.
FINDING SIDES WITH TRIGONOMETRYHARDQuestion 28
Opposite=20 and adjacent=21. What is cos θ?
Which choice is correct?
A) 20/29
B) 21/29
C) 20/21
D) 21/20
Show full solution
Correct answer: B) 21/29
The hypotenuse is 29.
SAT trap: Use adjacent over hypotenuse.
FINDING SIDES WITH TRIGONOMETRYHARDQuestion 29
If tan θ=3/4 and adjacent=20, find the opposite side.
Which choice is correct?
A) 12
B) 15
C) 16
D) 25
Show full solution
Correct answer: B) 15
3/4=x/20 gives x=15.
SAT trap: Scale the ratio.
FINDING SIDES WITH TRIGONOMETRYHARDQuestion 30
If cos θ=8/17 and hypotenuse=34, find the adjacent side.
Which choice is correct?
A) 8
B) 16
C) 17
D) 26
Show full solution
Correct answer: B) 16
8/17=x/34 gives x=16.
SAT trap: The scale factor is 2.
How Are Special Angles and Exact Values Tested?
Use 30°, 45°, and 60° values and complementary-angle relationships.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 31
What is sin 45°?
Which choice is correct?
A) 1/2
B) √2/2
C) √3/2
D) 1
Show full solution
Correct answer: B) √2/2
sin 45°=√2/2.
SAT trap: Use a 45-45-90 triangle.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 32
What is cos 45°?
Which choice is correct?
A) 1/2
B) √2/2
C) √3/2
D) 1
Show full solution
Correct answer: B) √2/2
cos 45°=√2/2.
SAT trap: Sine and cosine match at 45°.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 33
What is tan 45°?
Which choice is correct?
A) 0
B) 1/2
C) 1
D) √3
Show full solution
Correct answer: C) 1
The legs are equal.
SAT trap: Tangent is opposite over adjacent.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 34
What is sin 60°?
Which choice is correct?
A) 1/2
B) √2/2
C) √3/2
D) 1
Show full solution
Correct answer: C) √3/2
Use the 30-60-90 ratio.
SAT trap: The side opposite 60° is the long leg.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 35
What is cos 30°?
Which choice is correct?
A) 1/2
B) √2/2
C) √3/2
D) 1
Show full solution
Correct answer: C) √3/2
cos 30°=√3/2.
SAT trap: Cos 30° equals sin 60°.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 36
What is tan 30°?
Which choice is correct?
A) 1/√3
B) 1
C) √3
D) 2
Show full solution
Correct answer: A) 1/√3
tan 30°=1/√3.
SAT trap: Do not invert it.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 37
What is tan 60°?
Which choice is correct?
A) 1/√3
B) 1
C) √3
D) 2
Show full solution
Correct answer: C) √3
tan 60°=√3.
SAT trap: Use the long leg over short leg.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 38
For complementary acute angles A and B, which identity is true?
Which choice is correct?
A) sin A=sin B
B) sin A=cos B
C) tan A=tan B
D) cos A=-sin B
Show full solution
Correct answer: B) sin A=cos B
Sine and cosine are cofunctions.
SAT trap: A+B=90°.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 39
If A+B=90° and sin A=7/25, what is cos B?
Which choice is correct?
A) 7/24
B) 7/25
C) 24/25
D) 25/7
Show full solution
Correct answer: B) 7/25
cos B=sin A.
SAT trap: Use complementary angles.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 40
If A+B=90° and tan A=5/12, what is tan B?
Which choice is correct?
A) 5/12
B) 12/5
C) 5/13
D) 12/13
Show full solution
Correct answer: B) 12/5
tan B=1/tan A.
SAT trap: Take the reciprocal.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 41
If sin θ=cos θ and θ is acute, what is θ?
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 90°
Show full solution
Correct answer: B) 45°
Sine and cosine are equal at 45°.
SAT trap: Use a 45-45-90 triangle.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 42
If tan θ=1 and θ is acute, what is θ?
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 75°
Show full solution
Correct answer: B) 45°
tan 45°=1.
SAT trap: Equal legs produce tangent 1.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 43
If sin θ=1/2 and θ is acute, what is θ?
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 90°
Show full solution
Correct answer: A) 30°
sin 30°=1/2.
SAT trap: Use exact values.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 44
If cos θ=1/2 and θ is acute, what is θ?
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 90°
Show full solution
Correct answer: C) 60°
cos 60°=1/2.
SAT trap: Do not confuse sine and cosine.
SPECIAL ANGLES AND EXACT VALUESHARDQuestion 45
If tan θ=√3 and θ is acute, what is θ?
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 75°
Show full solution
Correct answer: C) 60°
tan 60°=√3.
SAT trap: Use exact tangent values.
Practice More SAT Geometry and Trigonometry
Build accuracy with exact values and right-triangle applications.
How Are Trigonometric Ratios Used in Applications?
Model heights, shadows, ramps, ladders, slopes, and coordinate triangles.
TRIGONOMETRY APPLICATIONSHARDQuestion 46
From 30 feet away, the angle of elevation to a building top is 45°. Find the height.
Which choice is correct?
A) 15
B) 30
C) 30√2
D) 60
Show full solution
Correct answer: B) 30
tan 45°=h/30=1.
SAT trap: The horizontal distance is adjacent.
TRIGONOMETRY APPLICATIONSHARDQuestion 47
A flagpole casts a 12-foot shadow at a 60° sun angle. Find its height.
Which choice is correct?
A) 6
B) 6√3
C) 12√3
D) 24
Show full solution
Correct answer: C) 12√3
h=12 tan 60°=12√3.
SAT trap: Shadow length is adjacent.
TRIGONOMETRY APPLICATIONSHARDQuestion 48
A ramp rises 3 feet over a run of 4 feet. What is sin θ?
Which choice is correct?
A) 3/4
B) 3/5
C) 4/5
D) 5/3
Show full solution
Correct answer: B) 3/5
The hypotenuse is 5.
SAT trap: Use rise over ramp length.
TRIGONOMETRY APPLICATIONSHARDQuestion 49
A line through the origin has slope 3/4. What is tan θ for its acute angle with the x-axis?
Which choice is correct?
A) 3/4
B) 4/3
C) 3/5
D) 4/5
Show full solution
Correct answer: A) 3/4
Slope=tan θ.
SAT trap: Use rise over run.
TRIGONOMETRY APPLICATIONSHARDQuestion 50
A line through the origin has slope √3. What acute angle does it make with the x-axis?
Which choice is correct?
A) 30°
B) 45°
C) 60°
D) 90°
Show full solution
Correct answer: C) 60°
tan θ=√3.
SAT trap: Use exact values.
TRIGONOMETRY APPLICATIONSHARDQuestion 51
A 20-foot guy wire is anchored 12 feet from a pole. What is cos θ at the ground?
Which choice is correct?
A) 3/5
B) 4/5
C) 12/20
D) Both A and C
Show full solution
Correct answer: D) Both A and C
12/20=3/5.
SAT trap: Equivalent ratios are equal.
TRIGONOMETRY APPLICATIONSHARDQuestion 52
A 13-foot ladder reaches 12 feet up a wall. What is tan θ at the ground?
Which choice is correct?
A) 5/12
B) 12/5
C) 12/13
D) 5/13
Show full solution
Correct answer: B) 12/5
The base is 5.
SAT trap: Find the missing side.
TRIGONOMETRY APPLICATIONSHARDQuestion 53
A right triangle has vertices (0,0),(8,0),(8,6). For the angle at (0,0), what is tan θ?
Which choice is correct?
A) 3/4
B) 4/3
C) 6/10
D) 8/10
Show full solution
Correct answer: A) 3/4
tan θ=6/8=3/4.
SAT trap: Use coordinate differences.
TRIGONOMETRY APPLICATIONSHARDQuestion 54
A right triangle has vertices (0,0),(5,0),(5,12). For the angle at (0,0), what is sin θ?
Which choice is correct?
A) 5/12
B) 5/13
C) 12/13
D) 12/5
Show full solution
Correct answer: C) 12/13
The hypotenuse is 13.
SAT trap: Recognize a 5-12-13 triangle.
TRIGONOMETRY APPLICATIONSHARDQuestion 55
A 15-foot ramp rises 3 feet. What is sin θ?
Which choice is correct?
A) 1/5
B) 1/4
C) 3/5
D) 5
Show full solution
Correct answer: A) 1/5
sin θ=3/15=1/5.
SAT trap: The ramp is the hypotenuse.
What Do Hard Mixed Trigonometry Questions Look Like?
Combine ratios, the Pythagorean theorem, identities, and area.
HARD MIXED TRIGONOMETRYHARDQuestion 56
If sin θ=8/17, what is tan θ?
Which choice is correct?
A) 8/15
B) 15/8
C) 8/17
D) 15/17
Show full solution
Correct answer: A) 8/15
The adjacent side is 15.
SAT trap: Use an 8-15-17 triangle.
HARD MIXED TRIGONOMETRYHARDQuestion 57
If cos θ=12/13, what is tan θ?
Which choice is correct?
A) 5/12
B) 12/5
C) 5/13
D) 12/13
Show full solution
Correct answer: A) 5/12
The opposite side is 5.
SAT trap: Use a 5-12-13 triangle.
HARD MIXED TRIGONOMETRYHARDQuestion 58
If tan θ=7/24, what is sin θ?
Which choice is correct?
A) 7/24
B) 7/25
C) 24/25
D) 25/7
Show full solution
Correct answer: B) 7/25
The hypotenuse is 25.
SAT trap: Use a 7-24-25 triangle.
HARD MIXED TRIGONOMETRYHARDQuestion 59
If tan θ=15/8, what is cos θ?
Which choice is correct?
A) 8/15
B) 8/17
C) 15/17
D) 17/8
Show full solution
Correct answer: B) 8/17
The hypotenuse is 17.
SAT trap: Use adjacent over hypotenuse.
HARD MIXED TRIGONOMETRYHARDQuestion 60
If sin θ=3/5, what is sin²θ+cos²θ?
Which choice is correct?
A) 3/5
B) 4/5
C) 1
D) 25/9
Show full solution
Correct answer: C) 1
Use the Pythagorean identity.
SAT trap: This identity always equals 1.
HARD MIXED TRIGONOMETRYHARDQuestion 61
If sin θ=5/13, what is cos²θ?
Which choice is correct?
A) 25/169
B) 144/169
C) 12/13
D) 1
Show full solution
Correct answer: B) 144/169
cos²θ=1-25/169.
SAT trap: The question asks for the squared value.
HARD MIXED TRIGONOMETRYHARDQuestion 62
If tan θ=2, what is tan(90°-θ)?
Which choice is correct?
A) 1/2
B) 1
C) 2
D) 4
Show full solution
Correct answer: A) 1/2
Use the reciprocal cofunction relationship.
SAT trap: Complementary tangents are reciprocals.
HARD MIXED TRIGONOMETRYHARDQuestion 63
A right triangle has hypotenuse 26 and sin θ=5/13. Find the adjacent side.
Which choice is correct?
A) 10
B) 20
C) 24
D) 25
Show full solution
Correct answer: C) 24
Scale a 5-12-13 triangle by 2.
SAT trap: Scale all sides equally.
HARD MIXED TRIGONOMETRYHARDQuestion 64
A right triangle has legs in ratio 3:5 and area 120. Find the longer leg.
Which choice is correct?
A) 10
B) 15
C) 20
D) 25
Show full solution
Correct answer: C) 20
Let legs be 3k and 5k. Then 7.5k²=120, so k=4.
SAT trap: Use the area to find the scale factor.
HARD MIXED TRIGONOMETRYHARDQuestion 65
A right triangle has legs in ratio 3:4 and area 96. Find the shorter leg.
Which choice is correct?
A) 6
B) 8
C) 12
D) 16
Show full solution
Correct answer: C) 12
Let legs be 3k and 4k. Then 6k²=96, so k=4.
SAT trap: Reject negative lengths.
What Do Student-Produced Responses Look Like?
Enter the requested ratio, side length, or angle.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 66
Opposite=9 and hypotenuse=15. What is sin θ as a decimal?
Enter your answer.
Show full solution
Correct answer: 0.6
9/15=0.6.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 67
Adjacent=12 and hypotenuse=13. What is the numerator of cos θ?
Enter your answer.
Show full solution
Correct answer: 12
cos θ=12/13.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 68
If tan θ=3/4 and adjacent=16, find the opposite side.
Enter your answer.
Show full solution
Correct answer: 12
3/4=x/16 gives x=12.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 69
A right triangle has hypotenuse 20 and angle 30°. Find the opposite side.
Enter your answer.
Show full solution
Correct answer: 10
The side opposite 30° is half the hypotenuse.
SAT trap: Enter only the requested numerical value.
STUDENT-PRODUCED RESPONSEMEDIUMQuestion 70
A line through the origin has slope 1. What acute angle does it make with the x-axis?
Enter your answer.
Show full solution
Correct answer: 45
tan θ=1, so θ=45°.
SAT trap: Enter only the requested numerical value.
Common SAT Trigonometry Mistakes
| Mistake | Correction |
|---|---|
| Confusing opposite and adjacent | Label sides relative to θ |
| Using the wrong ratio | Remember SOH-CAH-TOA |
| Ignoring a missing side | Use the Pythagorean theorem first |
| Mixing 30° and 60° | Use the 1:√3:2 ratio |
Two-Week Study Plan
| Days | Focus |
|---|---|
| 1-3 | Q1-Q15 |
| 4-7 | Q16-Q30 |
| 8-10 | Q31-Q45 |
| 11-14 | Q46-Q70 and review |
Frequently Asked Questions About SAT Trigonometric Ratios Practice Questions
Are trigonometric ratios tested on the Digital SAT?
Yes. They appear in Geometry and Trigonometry questions.
What does SOH-CAH-TOA mean?
Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.
How do I identify the hypotenuse?
It is opposite the 90° angle.
What are the special-angle values?
Use 30-60-90 and 45-45-90 triangle ratios.
How is slope connected to trigonometry?
For an acute line angle, slope=tan θ.
What is the complementary-angle identity?
For complementary acute angles, sin A=cos B.
What identity connects sine and cosine?
sin²θ+cos²θ=1.
How many questions should I practice?
Practice ratios, special triangles, side finding, exact values, slopes, and word problems.
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