Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 1 - Section 1.1 - Angles, Degrees, and Special Triangles - 1.1 Problem Set: 55

Answer

Length of escalator $\approx$ 23.1 feet

Work Step by Step

This is an classic example of 30°–60°–90° triangle in which side opposite 60° is given and length of longest side is to be calculated- The longest side of a 30°–60°–90° triangle is twice the shortest side and the side opposite the 60° angle is $\sqrt 3$ times the shortest side. Given that Side opposite 60° = 20 Therefore Shortest side = $\frac{Side opposite 60°}{\sqrt 3}$ = $\frac{20}{\sqrt 3}$ Shortest side = $\frac{20\times\sqrt 3}{ \sqrt 3\times\sqrt 3}$ = $\frac{20\sqrt 3 }{3} $ Longest Side = 2 $\times $ shortest side = 2$\times\frac{20\sqrt 3}{3}$ Longest Side = $\frac{40\sqrt 3 }{3} \approx 23.1$ Therefore length of escalator $\approx 23.1$ feet
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