Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 7 - Applications of Trigonometry and Vectors - Summary Exercises on Applications of Trigonometry and Vectors - Page 345: 6


The height of the plane is 7203.6 feet

Work Step by Step

Let $C$ be the plane's position. Then A, B, and C form a triangle. The angle $B = 180^{\circ}-57^{\circ} = 123^{\circ}$ The angle $C = 180^{\circ}- 52^{\circ}-123^{\circ} = 5^{\circ}$ We can use the law of sines to find the length of the side $AC$: $\frac{AC}{sin~B} = \frac{AB}{sin~C}$ $AC = \frac{(AB)~sin~B}{sin~C}$ $AC = \frac{(950~ft)~sin~123^{\circ}}{sin~5^{\circ}}$ $AC = 9141.5~ft$ We can draw a vertical line from the plane's position straight down to the ground. The length of this line $h$ is the height of the plane. Let $D$ be the point where this line meets the ground. Then A, C, and D form a right triangle. We can find the height $h$: $\frac{h}{AC} = sin~52^{\circ}$ $h = (AC)~sin~52^{\circ}$ $h = (9141.5~ft)~sin~52^{\circ}$ $h = 7203.6~ft$ The height of the plane is 7203.6 feet
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