BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.6, Problem 50E
To determine

To find: The height of the flagpole to the nearest inch.

Expert Solution

Answer to Problem 50E

The height of the flagpole is 32 ft 4 inch.

Explanation of Solution

Given:

The length of each wire is 5 ft longer than the height of pole.

The distance between the wires fixed on the ground is equal to the length of one wire.

Calculation:

Let x be the height of flagpole.

Tabulate the given information algebraically.

In wordsIn Algebra
Height of flagpolex
Length of wirex+5
Distance between pole and a guy wirex+52

Table (1)

Model the equation for the above information as follows.

From the given data, there is an isosceles triangle appear here.

Use Pythagoras theorem to find the length of the flagpole as follows.

(Distancebetweenpoleandwire)2+(Lengthofpole)2=(Lengthofwire)2(x+52)2+x2=(x+5)2(x+5)2+4x2=4(x+5)24x2=3(x+5)2

On further simplification,

4x2=3(x2+25+10x)4x2=3x2+75+30xx230x75=0

Use quadratic formula x=b±b24ac2a to find the value of x.

x=(30)±(30)24×1×(75)2×1=30±900+3002=30±12002=30±34.642

On further simplification,

x=30+34.642,x=3034.642x=32.32,x=2.32

The height of the pole cannot be negative.

So the height of the pole, x=32.32.

Thus, the height of the flagpole is 32 ft 4 inch.

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