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? 10 ft 3 ft options: 16.7°, 17.5°, 72.5°, 73.3°

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the tangent of an angle \(x\) is given by \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the side opposite to angle \(x\) is \(3\) (length of the shorter beam) and the side adjacent to angle \(x\) is \(10\) (length of the longer beam). So, \(\tan x=\frac{3}{10}\).

Step2: Solve for \(x\)

We know that if \(\tan x = a\), then \(x=\arctan(a)\). Since \(a = \frac{3}{10}=0.3\), we have \(x=\arctan(0.3)\). Using a calculator, \(x\approx16.7^{\circ}\)

Answer:

\(16.7^{\circ}\) (First option)