Chapter 12, Problem 2E

To determine

To calculate: Unknown angle of the given triangle.

Answer to Problem 2E

(J) $33.6°$

Explanation of Solution

Given information: A diagram of right-angled triangle is given. Also, the hypotenuse as $12$ ft and the adjacent with respect to the angle is given as $10$ ft.

  

Formula used: For the angle $\theta$ in the given triangle, $\cos (\theta )=\left(\frac{b}{c}\right)$ . Where $b$ is the adjacent and $c$ is the hypotenuse of the triangle.

Calculation: Plug the value of adjacent and hypotenuse in $\cos (\theta )=\left(\frac{b}{c}\right)$ , we get.

  $\begin{array}{l}\cos (\theta )=\left(\frac{b}{c}\right)\\ \cos (\theta )=\left(\frac{10}{12}\right)\\ \cos (\theta )=0.833\end{array}$

Now, taking arccos both sides, we get.

  $\begin{array}{l}\cos (\theta )=0.833\\ {\cos }^{-1}(\cos (\theta ))={\cos }^{-1}(0.833)\\ \theta =32.591\\ \theta =33.6°\end{array}$

So, the unknown angle of the given triangle $33.6°$