Applying the Inverse Cosine to a Right Triangle

Solve the triangle in Figure 8 for the angle $θ .$

Figure 8

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Because we know the hypotenuse and the side adjacent to the angle, it makes sense for us to use the cosine function.

$\begin{array}{l} \cos θ = \frac{9}{12} & \begin{matrix} \end{matrix} \\ θ = \cos^{- 1} (\frac{9}{12}) & \begin{matrix} \end{matrix} Apply definition of the inverse . \\ θ \approx 0.7227 or about 41.4096° & \begin{matrix} \end{matrix} Evaluate . \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the triangle in Figure 9 for the angle $θ .$

Figure 9

How did it go?