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# Viewing angles An auditorium with a flat floor has a large

ISBN: 9780321570567 2

## Solution for problem 41E Chapter 4.4

Calculus: Early Transcendentals | 1st Edition

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Problem 41E

Viewing angles An auditorium with a flat floor has a large screen on one wall. The lower edge of the screen is 3 ft above eye level and the upper edge of the screen is 10 ft above eye level (see figure). How far from the screen should you stand to maximize your viewing angle?

Step-by-Step Solution:

Solution 41E Step 1: Suppose the eye is x feet away from the screen then the angle to the top of the screen is tan = 10 (since angle of elevation is given by tan = opposite si)e 1 x adjacent side = tan ( 1 10) 1 x angle to bottom of the screen is tan = 3 (since angle of elevation is given by tan = opposite si)e 2 x adjacent side 1 3 =2tan ( ) x So the viewing angle from x feet away is given by = -1 2 1 10 1 3 = tan ( x )-tan ( ) x Step 2: In order to get maximum viewing angle,we need to find critical point in order to find critical number we need to make first derivative equal to 0 d dx= 0 d 1 10 1 3 dx( tan ( x )-tan ( ))x0 1 d 10 1 d 3 1+(2)2dx x) 1+(2)2dx x)=0 10 3 x x x2 102 1+(2)2=0 1+(x2) x x2 x3 x +100 x +9=0 ( x2 ) (x2 ) 10 3 (x +100)+ x +9 =0

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##### ISBN: 9780321570567

This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The full step-by-step solution to problem: 41E from chapter: 4.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: Screen, level, viewing, edge, eye. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. Since the solution to 41E from 4.4 chapter was answered, more than 588 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Viewing angles An auditorium with a flat floor has a large screen on one wall. The lower edge of the screen is 3 ft above eye level and the upper edge of the screen is 10 ft above eye level (see figure). How far from the screen should you stand to maximize your viewing angle?” is broken down into a number of easy to follow steps, and 55 words.

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