Practice Right Triangle Trigonometry in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The three primary trigonometric ratios—sine, cosine, and tangent—defined as ratios of specific sides in a right triangle.

Imagine a ramp leaning against a wall. The steepness depends on the ratio of how high the wall is to how long the ramp is. Trigonometry gives names to these ratios: sine is how high compared to the ramp, cosine is how far along the ground compared to the ramp, and tangent is how high compared to how far along the ground. No matter how big or small the ramp, if the angle is the same, these ratios stay the same.

Example 1

easy
In a right triangle, the angle \theta = 30°, and the hypotenuse is 10. Find the lengths of the opposite and adjacent sides.

Example 2

medium
A ladder 13 feet long leans against a wall. The base of the ladder is 5 feet from the wall. Find the angle the ladder makes with the ground (to the nearest degree).

Example 3

easy
In a right triangle with angle \theta = 45° and hypotenuse = 8, find both legs.

Example 4

hard
From the top of a 50-meter tall lighthouse, the angle of depression to a boat is 32°. How far is the boat from the base of the lighthouse (to the nearest meter)?
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