$\"\"$

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Consider the radio tower location is $\"\"$ .

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A radio tower located 38 miles along industrial parkway and it broadcast radius is 30 miles.

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C represents the rightmost point on the interstate within the broadcasting radius.

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Draw the diagram with above specifications.

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$\"\"$

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Consider triangle $\"\"$ .

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Law of sines : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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The sum of the angles in any triangle is $\"\"$ .

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The two angles are $\"\"$ and $\"\"$ .

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The remaining angle $\"\"$ .

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$\"\"$

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Law of sines : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Consider triangle $\"\"$ .

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Since triangle $\"\"$ is an isosceles triangle, therefore $\"\"$ .

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The angle $\"\"$ , then $\"\"$ .

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Law of sines : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore vehicles can pick up the broadcasting signal for $\"\"$ miles along the interstate.

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$\"\"$

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Therefore vehicles can pick up the broadcasting signal for $\"\"$ miles along the interstate.