## Trigonometry (11th Edition) Clone

Published by Pearson

# Chapter 7 - Applications of Trigonometry and Vectors - Section 7.1 Oblique Triangles and the Law of Sines - 7.1 Exercises - Page 303: 43

#### Answer

We calculate that the distance between Bochum and the moon is 419,000 km, which is similar to the known distance of 406,000 km

#### Work Step by Step

We can form a triangle with Bochum, Donaueschingen, and the moon. Let $D$ be the angle at Donaueschingen. Then $D = 180^{\circ}-52.7430 = 127.2570^{\circ}$ We can find the angle $M$ at the moon: $B+D+M = 180^{\circ}$ $M = 180^{\circ}-B-D$ $M = 180^{\circ}-52.6997^{\circ}- 127.2570^{\circ}$ $M = 0.0433^{\circ}$ We can find the length of side $d$ which is the distance from Bochum to the moon: $\frac{d}{sin~D} = \frac{m}{sin~M}$ $d = \frac{m~sin~D}{sin~M}$ $d = \frac{(398~km)~sin~(127.2570^{\circ})}{sin~(0.0433^{\circ})}$ $d = 419,000~km$ We calculate that the distance between Bochum and the moon is 419,000 km, which is similar to the known distance of 406,000 km.

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.