Question

a theater production group is making frames to support wall - like props. three - foot beams form right triangles with 10 - foot beams to allow them to stand, as shown in the image. what is x, the angle at which the diagonal beam meets the 10 - foot beam at the top of the frame? 16.7° 17.5° 72.5° 73.3°

Explanation:

Step1: Recall tangent function

In a right - triangle, $\tan(x)=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to angle $x$ is 3 feet and the adjacent side is 10 feet. So, $\tan(x)=\frac{3}{10}$.

Step2: Find the angle

We need to find $x$. Using the inverse - tangent function, $x = \tan^{- 1}(\frac{3}{10})$.
Calculating $\tan^{-1}(0.3)$ using a calculator in degree mode, we get $x\approx16.7^{\circ}$.

Answer:

16.7°