Question

finding an unknown angle
the scaffolding for a construction site is shown in the diagram
determine the measure of the angle where the floor of the second landing of the scaffolding meets the diagonal brace, x, to the nearest degree

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle with adjacent side $a = 7$ ft and hypotenuse $c=8.75$ ft. We use the cosine function $\cos(x)=\frac{a}{c}$.

Step2: Calculate the cosine value

$\cos(x)=\frac{7}{8.75}=0.8$.

Step3: Find the angle

$x = \cos^{-1}(0.8)$. Using a calculator, $x\approx36.87^{\circ}\approx37^{\circ}$ (to the nearest degree).

Answer:

$37^{\circ}$