Two boats are equidistant from a lighthouse. The boats are 30 miles apart. The angle formed between the two boats, with the lighthouse as the vertex, measures 40°. Approximately how far is each boat from the lighthouse?

The lighthouse and the two boats form an isosceles triangle with equal sides of length r and a 40° angle at the lighthouse. Splitting the triangle in half gives a right triangle with opposite side 15 miles and angle 20°, so sin(20°) = 15/r and r = 15/sin(20°) ≈ 43.9 miles. Each boat is approximately 44 miles from the lighthouse.

AI-written and checked against the verified answer.