Answered: Building A 4865 ft Building B Building…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

You are asked to find the distance from building A to building B in feet given the following information. Also compute the angle at B if it is a right triangle as shown

Building A
4865 ft
Building B
Building C
1 mile

Expert Solution

Step 1

The free-body diagram,

Step 2

As per the law of triangle by Lami's theorem,

$\frac{A}{\sin α} = \frac{B}{\sin β} = \frac{C}{\sin γ} \frac{A}{\sin α} = \frac{B}{\sin β} = C$

Where, Sin 90 = 1

Now,

$\tan α = \frac{4865 f t}{5280 f t} \tan α = 0.921 α = \tan^{- 1} 0.921 α = 62.2 °$

For find distance between building A and B,

$\frac{A}{\sin α} = C \frac{4865 f t}{\sin 62.2 °} = C C = 5500 f t$

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