a shelf is supported on a wall by a triangular bracket with the dimensi…
\( 42.5 \)
Question
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.
°
Solution Steps
-
Understand the question
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, \( \theta\approx 42.5^\circ \) -
Final answer
\( 42.5 \)
Answer
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
\( 42.5 \)
Question Image
Click to enlargeQuestion Analysis
Subject
mathematics
Sub Subject
geometry
Education Level
high school
Difficulty
unspecified
Question Type
with image, calculation
Multi Question
No
Question Count
1
Analysis Status
completed
Analyzed At
2026-01-30T12:07:39
OCR Text
Show OCR extraction
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. °
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