## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 13, Trigonometric Ratios and Functions - 13.5 Apply the Law of Sines - 13.5 Exercises - Skill Practice - Page 886: 2

#### Answer

See answer below.

#### Work Step by Step

When the values for $a,b,A$ are given then by the Law of sines: $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$, $\sin B$ can be found. 1) There will exist no triangles, when the sine of the angle $B$ has a value such that the $\sin$ rule is not followed. This means that $B \geq 180^{\circ}-A$ 2) There will exist One Triangle when $B=90^{\circ}$. 3) There will exist two triangles, when sine of the angle $B$ is the same for two different values of $c$.

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