Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.1 - The Law of Sines - Exercise Set - Page 720: 32


There is no triangle with the provided measurements.

Work Step by Step

Using the ratio $\frac{a}{\sin A}$, or $\frac{1.4}{\sin 142{}^\circ }$, We will use the law of sines to find B. $\begin{align} & \frac{b}{\sin B}=\frac{a}{\sin A} \\ & \frac{1.4}{\sin 142{}^\circ }=\frac{2.9}{\sin B} \\ & \sin B=\frac{2.9\sin 142{}^\circ }{1.4} \\ & B\approx 1.28 \end{align}$ As we know that the sine ratio can never exceed 1, there is no angle B for which $\sin B=1.28$. Thus, there is no triangle with the provided measurements.
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