The inverse trigonometric functions \(\sin^{-1}(x), cos^{-1}(x), tan^{-1}(x), \) are used to find the unknown measure of an angle of a right triangle when two side lengths are known.

**Step 1**

Identify the sides in relation to the angle. In the diagram above, 6750 is the *adjacent side *in relation to angle \(a^{\circ}\), and 8100 is the *hypotenuse side*.

**Step 2**

Use the appropriate trigonometric ratio. Since the *adjacent* and *hypotenuse *sides are given, \(\cos^{-1}(x)\) is the appropriate inverse function.

**Step 3**

Perform the Calculations. \[\cos^{-1}\left(\frac{6750}{8100}\right) = 33.557^{\circ} \simeq 33.6^{\circ} \]

Take note that the angle setting in your calculator will determine the output measurement. Setting your calculator to *degrees* will give an answer in *degrees. *Whereas, *radian* mode will calculate answer in terms of *radians*.

Designed by Matthew Cheung. This work is licensed under a

Creative Commons Attribution 4.0 International License.