Using a Trigonometric Ratio to Find an Angle in a Right Triangle

Problem: Given the right triangle in the figure below with side a = 9 ft and side b = 11 ft, use a trigonometric ratio to find the measure of angle A to the nearest tenth.

Solution: We first notice that the two sides we have values for are a = 9 ft and side b = 11 ft. Side a is opposite angle A, and side b is adjacent to angle A.

Thus we know

To solve for the measure of angle A, we use inverse tangent, entering the following keypresses in our TI-84 calculator. The screen is shown below the keypresses.


NOTE: If you try the above and get a fractional number instead, that means that your calculator is in radian mode instead of degrees. Press mode and be sure degrees is highlighted as shown below.


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