Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 5 - Section 5.4 - The Pythagorean Theorem - Exercises - Page 253: 20

Answer

32 ft

Work Step by Step

The length of the bridge is 136 ft, so each half of the bridge is 68 ft. The space between the endpoints of the bridge remains the same at 136 ft, with a gap in the middle of 16 ft. Dividing this per side, that would mean that half the raised bridge would be over (136 - 16) ÷ 2 ft, or 60 ft. 68 ft will form the hypotenuse, with 60 ft and x ft forming the legs of the right triangle. We solve for x to find the height the bridge is raised. x2 + 60$^{2}$ = 68$^{2}$ Subtract 60$^{2}$ from each side x$^{2}$ = 68$^{2}$ - 60$^{2}$ x$^{2}$ = 4624 - 3600 x$^{2}$ = 1024 x = 32
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