### Steps to Finding Angles When Two Sides Are Known

**Example:** Use the two known side lengths of the right triangle below to find the angles of the triangle.

*Remember *: The function table can be used to find an angle when you know two side lengths of a right triangle.

Follow the steps below.

**First:** Mark the reference angle and name the sides for that angle.

**Second:** Look at the three functions and decide which one will work with the known sides. Replace the ratio with the leg lengths of the triangle and calculate the problem.

Tangent is the correct choice. It is the only function of the three which uses both known sides.

**Third:** Use the correct arc function key to find the degrees of the reference angle.

With the answer (0.392857142) still in the display, push the key. The display will show 21.44773633, the degrees in the reference angle. If we round the number off to the nearest one-half degree, it becomes **21.5° .**

**Fourth:** Find the degrees of the other angle.
*Remember *: The sum of the three angles of any triangle will **always** equal 180° .

Since the two angles (other than the right angle) equal a total of 90° , subtract the known angle from 90° to find the degrees of the other angle.

**Finding the Angles When Two Sides Are Known: Practice**

Find the measurement for both angles of each right triangle. Round off each answer to the nearest 1/2° .

(1) Opp = 22" Hyp = 34"
(2) Adj = 19.375" Opp = 27.5"
(3) Adj - 64.9375" Hyp = 78.4375"
(4) Opp = 14.5" Adj = 29.685"
(5) Hyp = 3' Opp = 2.5'