Test
Applications of trigonometry
Dynamic height, distance, slope, shadow and motion problems using trigonometric ratios.
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Sample questions
- An observer is ___ m from a building. The tangent of the elevation angle is ___. Find the height.
- A road rises ___ m over ___ m horizontally. What is the percentage grade?
- A plane travels ___ m along a path whose angle has sine ___. How high does it climb?
- An object casts a ___ m shadow and the sun angle has tangent ___. Find the height.
- An object is ___ m high and the observation angle has tangent ___. Find the horizontal distance.
Applications of trigonometry
Trigonometry finds inaccessible heights and distances by modelling a right triangle. An angle of elevation is measured upward from the horizontal, while an angle of depression is measured downward from it.
Modelling a practical problem
Draw a diagram and label the known angle, horizontal distance and required height. Select sine, cosine or tangent from the sides involved. If the observer is above ground, add the eye height only at the end; assess whether the result is realistic and round appropriately.
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