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 - Section 7.1 Oblique Triangles and the Law of Sines - 7.1 Exercises - Page 301: 7

Answer

Sufficient information

Work Step by Step

$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{ \sin C}$ Suppose that $\angle A$ and $\angle B$ are known. Then $m\angle C=180-(m\angle A+m\angle B)$ Since $c$ being included side of angle A and angle B is already known, then $ \frac{c}{ \sin\angle C}$ is a known quantity. Let $ \frac{c}{ \sin\angle C}= k$ Now using the Law of Sine: $\frac{a}{\sin\angle A}=\frac{c}{\sin\angle C}$ $a=\frac{c}{\sin\angle C} \times \sin\angle A=k\sin\angle A$ Similarly $b$ may be calculated as $b=k \sin\angle B$ So there is sufficient information to solve the triangle.
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