Right Triangle Trigonometry Exercise 3

Here is the third of three examples. Use the triangle to the right for reference. The solution is at the bottom of the post. A trig table and the trig wheels are also included.

Angle 1 is 25° and the length of side A is 24. Find the lengths sides B and C, and angle 2.

This solution demonstrates one of a number of possible ways to come to the values in bold; the important thing is to arrive at the same values shown for each unknown.

Angle 1 is 25° and the length of side A is 24. Find the lengths sides B and C, and angle 2.

Angle 2 is found by subtracting 25° from 90°. Angle 2 is equal to 65°.

The hypotenuse (side B) can be found by dividing the length of side adjacent to angle 1 (side A), 24, by the cosine of angle 1. The cosine of angle 1 is 0.9063. The hypotenuse is equal to 24 divided by 0.9063, or 26.48.

The side opposite angle 1 (side C) can be found by multiplying the tangent of angle 1 by the adjacent side A. The tangent of 25° is 0.4663. Multiplying 0.4663 by 24 is equal to 11.19.