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题目

解题步骤

1. 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.
   °

2. 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, \( \theta\approx 42.5^\circ \)

3. Final answer

   \( 42.5 \)

答案

Question Analysis

OCR Text

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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