Question

15,312 Learners found this answer helpful

a shelf is supported on a wall by a triangular bracket with the dimensions shown in the diagram.
what is the measure of the angle formed by the wall and the bottom of the bracket to the nearest tenth of a degree?
enter the correct answer in the box.
°

Explanation:

Step1: Identify the sides

We have a right triangle where the adjacent side to the angle (wall side) is \( 13\frac{1}{8} = \frac{105}{8} = 13.125 \) in and the opposite side (horizontal side) is 12 in. We can use the tangent function \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \).

Step2: Calculate the tangent of the angle

\( \tan(\theta)=\frac{12}{13.125} \)
\( \tan(\theta) \approx 0.9142857 \)

Step3: Find the angle

Take the arctangent (inverse tangent) of 0.9142857.
\( \theta=\arctan(0.9142857) \)
Using a calculator, \( \theta\approx 42.5^\circ \)

Answer:

\( 42.5 \)