QQuestionCivil Engineering
QuestionCivil Engineering
What is the multiplier for an offset using 45 -degree bends?
A. 1.41
B. 1.73
C. 2.00
D. 2.45
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Answer
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Step 1:I'll solve this step by step with precise LaTeX formatting:
Step 2:: Understanding the Problem
The problem asks about the multiplier for an offset using 45 -degree bends. This typically relates to trigonometric calculations involving right-angle or diagonal offsets.
Step 3:: Trigonometric Analysis
\sin(45°) = \cos(45°) = \frac{1}{\sqrt{2}} \approx 0.7071
For a 45 -degree bend, we can use trigonometric principles. At a 45 -degree angle, the sine and cosine are equal.
Step 4:: Calculating the Multiplier
\text{Multiplier} = \sqrt{1^{2} + 1^{2}} = \sqrt{2} \approx 1.41
The multiplier for a 45 -degree offset can be calculated using the Pythagorean relationship:
Step 5:: Verification
This matches the trigonometric principle that at 45 degrees, both sides of a right triangle are equal, and the hypotenuse is $$\sqrt{2}$$ times the length of a side.
Final Answer
The multiplier for an offset using 45 -degree bends is 1.41, which corresponds to option A.
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