Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.7 - Modeling with Equations - 1.7 Exercises - Page 77: 52

Answer

The flagpole's height is approximately $388in$

Work Step by Step

Let's imagine a triangle on this image. It will be equilateral triangle (As shown on the image). Let's also consider that the pole is $h$. Each side will be equal to $(h+5)ft$. According to one of the characteristics of a right angled triangle, the leg (side) opposite to $30°$ angle equals to half of hypotenuse. Which means that it is $\frac{h+5}{2}ft$ Now we can easily find flagpole height using the Pythagoras Theorem (Let's consider flagpole height as $h$) : $(\frac{h+5}{2})^2+h^2=(h+5)^2$ $\frac{h^2+10h+25}{4}+h^2=h^2+10h+25$ $h^2+10h+25=40h+100$ $h^2-30h-75=0$ $D = b^2-4ac = (-30)^2 - 4\times(-75)=900+300=1200$ $h_1 = \frac{-b-\sqrt{D}}{2a}=\frac{30-\sqrt{1200}}{2}$; This is a negative number and a length can't be negative number, so we can simply cross out this result. $h_2 = \frac{-b+\sqrt{D}}{2a}=\frac{30+\sqrt{1200}}{2}=15+10\sqrt3\approx32.32$ The flagpole is $32.32ft\approx387.84\approx388in$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.