Trig Ratios in Right Triangles – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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To calculate unknown side lengths and non-right angles of right triangles, trigonometric ratios are the keys to your success.

Just to refresh your memory, right triangles have a 90 degree angle. Look for the box in the corner to indicate a right angle. The side opposite the right angle is the hypotenuse, and the other sides are adjacent or opposite, depending on which angle you are considering.

The trig ratios you will use the most are sine, cosine, and tangent. Sine is the ratio of opposite to hypotenuse, cosine is the ratio of adjacent to hypotenuse, and tangent is the ratio of sine to cosine. Which ratio do you use to solve for an unknown measurement? That depends on what information is given in a problem. To help you solve problems, you’ll want to use a calculator that has the trig ratios or use a chart of the ratios.

Why do you study trig ratios? The ratios are very useful to solve real world problems. Before you hike up a steep mountain trail, do you want to know the distance of the trail? If you know the height of the mountain and one of the non-right angles, with the trig ratios you can calculate the measurement. Maybe you forgot to bring your calculator along on the hike – still it’s awesome to know that you can figure this out. To learn more, watch this video.

Define trigonometric ratios and solve problems involving right triangles


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Exercises in this Practice Problem
Find the trigonometric ratio that describes the angle of the given right triangle.
Evaluate the height of the Statue of Liberty using trigonometric ratios.
Solve for the height of each tree.
Determine the distance to the Eiffel Tower.
Identify the properties of right triangles.
Calculate the side lengths and angles of the right triangle.