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Use the figure below and the given information for Questions #5, #6 and #7

Use the figure below and the given information for Questions #5, #6 and #7-example-1

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ANSWER

18.1

Step-by-step explanation

AC is the shortest leg of triangle CAD. The hypotenuse is AD = 30 and AC is the opposite leg to the given angle, m∠ADC = 37°.

We can find the length of side AC using the sine of the given angle,


\begin{gathered} \sin 37\degree=(AC)/(AD) \\ \\ \sin 37\degree=(AC)/(30) \end{gathered}

Solving for AC,


AC=30\sin 37\degree=18.1

Hence, the length of AC is 18.1.

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