Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 2 - Acute Angles and Right Triangles - Section 2.5 Further Applications of Right Triangles - 2.5 Exercises: 33

Answer

The height of the pyramid is 114 feet

Work Step by Step

Let $x$ be the distance from the vertical line to the first point. We can write an expression for the height $h$: $\frac{h}{x} = tan~35.5^{\circ}$ $h = x~tan~35.5^{\circ}$ We can use the second point to write another equation for the height $h$: $\frac{h}{x+135} = tan~21.167^{\circ}$ $h = (x+135)~tan~21.167^{\circ}$ We can equate the two expressions to find $x$: $x~tan~35.5^{\circ} = (x+135)~(tan~21.167^{\circ})$ $0.713~x = 0.387~x+52.27$ $0.713~x - 0.387~x = 52.27$ $x = \frac{52.27}{0.326}$ $x = 160~ft$ We can use the first equation to find $h$: $h = x~tan~35.5^{\circ}$ $h = (160~ft)~tan~35.5^{\circ}$ $h = 114~ft$ The height of the pyramid is 114 feet
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