Precalculus (6th Edition) Blitzer

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

Chapter 6 - Mid-Chapter Check Point - Page 756: 3


This type of triangle with the given measurements does not exist.

Work Step by Step

The given angles and side of the triangle are provided below: $A=65{}^\circ,a=6,b=7$ Using the law of sines, we will find the angle B of the triangle. That is, $\begin{align} & \frac{\sin A}{a}=\frac{\sin B}{b} \\ & \frac{\sin 65{}^\circ }{6}=\frac{\operatorname{sinB}}{7} \end{align}$ Therefore, $\begin{align} & \operatorname{sinB}=7\times \frac{\sin 65{}^\circ }{6} \\ & \operatorname{sinB}=1.0574 \end{align}$ The function sine can’t exceed the value 1. Therefore, $\operatorname{sinB}=1.0574$ is not possible. Thus, there does not exist any triangle of this type with the given measurements.
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