# Chapter 5 - Section 5.5 - Trigonometric Equations - Exercise Set - Page 706: 166

The value of $a$ is $45.20$.

#### Work Step by Step

Solve the provided expression for a, \begin{align} & \frac{a}{\sin 46\text{ }\!\!{}^\circ\!\!\text{ }}=\frac{56}{\sin 63\text{ }\!\!{}^\circ\!\!\text{ }} \\ & a=\frac{56\times \sin 46\text{ }\!\!{}^\circ\!\!\text{ }}{\sin 63\text{ }\!\!{}^\circ\!\!\text{ }} \end{align} Then, calculate the value of $\sin 46\text{ }\!\!{}^\circ\!\!\text{ }$ and $\sin 63\text{ }\!\!{}^\circ\!\!\text{ }$ on the calculator as: $\sin 46\text{ }\!\!{}^\circ\!\!\text{ }=0.7193398$ and $\sin 63\text{ }\!\!{}^\circ\!\!\text{ }=0.891006524$ Now, use these values in the above expression, \begin{align} & a=\frac{56\times 0.7193398}{0.891006524} \\ & =\frac{40.2830288}{0.891006524} \\ & =45.2107 \end{align} And round off to the nearest decimal. $a=45.20$. Thus, the value of $a$ is $45.20$.

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