Exercise 6.1.6 solution

We know that two of the three angle of the triangle are \(30^\circ\) and \(180^\circ-50^\circ=130^\circ\), so the third angle is \(180^\circ-30^\circ-130^\circ=20^\circ\).

Let \(x\) denote the distance to the lighthouse.

Then, \(\dfrac{x}{\sin30^\circ}=\dfrac{2}{\sin20^\circ}\), so \(x=\dfrac{2\sin30^\circ}{\sin20^\circ}=2.92\) miles.

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