Question

Find the indicated side of the triangle. b a 30° 12. b = [?] o Enter

Answer 1

`\begin{gathered} \text{Given angle 30}^o, \\ \text{the hypotenuse is b} \\ \text{the opposite is a} \\ the\text{ adjacent is 12} \end{gathered}`
`\begin{gathered} \text{from SOH CAH TOA} \\ \tan \theta=(opposite)/(adjacent) \\ \tan 30=(a)/(12) \\ a=12\tan 30 \\ a=12(\frac{1}{\sqrt[]{3}}) \\ a=\frac{12}{\sqrt[]{3}} \end{gathered}`
`\begin{gathered} \cos \theta=(adjacent)/(hypotenuse) \\ \cos 30=(12)/(b) \\ b=(12)/(\cos 30) \\ b=\frac{12*2}{\sqrt[]{3}} \\ b=\frac{24}{\sqrt[]{3}} \end{gathered}`