Trigonometry (10th Edition)

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

Chapter 2 - Acute Angles and Right Triangles - Section 2.3 Finding Trigonometric Function Values Using a Calculator - 2.3 Exercises: 69a

Answer

(a) $c_{2}$ = 2.148 x $10^{8}$ $\frac{m}{s}$

Work Step by Step

For this problem, we use the following information: $\frac{c_{1}}{c_{2}}$ = $\frac{\sin\theta_{1}}{\sin\theta_{2}}$ $c_{1}$ = 3 x $10^{8}$ $\frac{m}{s}$ Now, we want to express the equation in terms of $c_{2}$. 1. $\sin\theta_{2}$ $\times$ ($\frac{c_{1}}{c_{2}}$) = $\sin\theta_{1}$ 2. ($\frac{\sin\theta_{2}}{\sin\theta_{1}}$) $\times$ $c_{1}$= $c_{2}$ From here, we can plug in the values to solve for $c_{2}$ (a) $\theta_{1}$ = 46$^{\circ}$ $\theta_{2}$ = 31$^{\circ}$ $c_{2}$ = $c_{1}$ $\times$ ($\frac{\sin\theta_{2}}{\sin\theta_{1}}$) $c_{2}$ = 3 x $10^{8}$ $\times$ ($\frac{\sin 31^{\circ}}{\sin 46^{\circ}}$) $c_{2}$ = 2.148 x $10^{8}$ $\frac{m}{s}$
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