$\"\"$

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Redraw the diagram:

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$\"\"$

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Consider the boat position is $\"\"$ , southbay and steep rock positions are $\"\"$ and $\"\"$ .

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The distance from the lighthouse at South Bay to the boat is $\"\"$ .

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The distance from the lighthouse at Steep Rock to the boat is $\"\"$ .

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Observe the figure:

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Two parallel lines are cut by a transversal, then then alternate interior angles are congruent.

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Therefore, $\"\"$

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$\"\"$ .

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From the figure $\"\"$ .

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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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$\"\"$

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Therefore , $\"\"$ and $\"\"$ and $\"\"$

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Law of sines : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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And $\"\"$ , $\"\"$ and $\"\"$

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Law of sines : $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Therefore ,The distance from the lighthouse at South Bay to the boat is $\"\"$ .

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The distance from the lighthouse at Steep Rock to the boat is $\"\"$ .

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$\"\"$

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The distance from the lighthouse at South Bay to the boat is $\"\"$ .

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The distance from the lighthouse at Steep Rock to the boat is $\"\"$ .