Assuming the dashed lines are parallel and perpendicular to the base, we can start by draw a third parallel line that passes through C and naming some distances:
Now, we can see that the given angles are alternate interior angles with respect to the angles formed by the new perpendicular line and the lines AC and BC:
Now, we can see that b and the base a + 24 are related with the tangent of 48°:
[tex]\tan 48\degree=\frac{a+24}{b}[/tex]
Also, b and a are related with the tangent of 17°:
[tex]\tan 17\degree=\frac{a}{b}[/tex]
We can solve both for b and equalize them:
[tex]\begin{gathered} b=\frac{a+24}{\tan48\degree} \\ b=\frac{a}{\tan17\degree} \\ \frac{a+24}{\tan48°}=\frac{a}{\tan17\degree} \\ a\tan 17\degree+24\tan 17\degree=a\tan 48\degree \\ a\tan 48\degree-a\tan 17\degree=24\tan 17\degree \\ a(\tan 48\degree-\tan 17\degree)=24\tan 17\degree \\ a=\frac{24\tan17\degree}{\tan48\degree-\tan17\degree}=\frac{24\cdot0.3057\ldots}{1.1106\ldots-0.3057\ldots}=\frac{7.3375\ldots}{0.8048\ldots}=9.1162\ldots \end{gathered}[/tex]
Now, we can relate a and x with the sine of 17°:
[tex]\begin{gathered} \sin 17\degree=\frac{a}{x} \\ x=\frac{a}{\sin17\degree}=\frac{9.1162\ldots}{0.2923\ldots}=31.18\ldots\approx31.2 \end{gathered}[/tex]
And x is the distance between A and C, the storm. Thus the answer is approximately 31.2 miles, fourth alternative.
