a theater production group is making frames to support wall - like props. three - foot beams form right…

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°

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°

Answer

Explanation:

Step1: Identify trig - function

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the opposite side to angle $x$ is 3 ft and the adjacent side is 10 ft. So, $\tan x=\frac{3}{10}$.

Step2: Solve for the angle

We use the inverse - tangent function, $x = \tan^{- 1}(\frac{3}{10})$. Using a calculator, $x=\tan^{-1}(0.3)\approx16.7^{\circ}$.

Answer:

$16.7^{\circ}$