Introduction:

In mathematics, "heights and distances" refers to the branch of trigonometry that deals with measuring and calculating heights, distances, and angles. It involves solving problems related to determining the height of an object, the distance between two objects, or the angle of elevation or depression.

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Formulas:

• Sine Formula: The sine formula relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.
  • sin θ = Opposite/Hypotenuse
• Cosine Formula: The cosine formula relates the ratio of the length of the side adjacent to an angle to the length of the hypotenuse in a right triangle.
  • cos θ = Adjacent/Hypotenuse
• Tangent Formula: The tangent formula relates the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle in a right triangle.
  • tan θ = Opposite/Adjacent
• Pythagorean Theorem: The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
  • a² + b² = c², where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse.
• Angle of Elevation: The angle of elevation is the angle between the horizontal line of sight and the line from the observer to an object above the horizontal line.
  • tan θ = Height/Distance