Trigonometry

Question

Can someone provide me a solution for this problem?

Two boats leave Whitby harbor at the same time. One boat heads 19km to its destination in Lake Ontario. The second boat heads on a course 70^o from the first boat and travels 11km to its destination. How far apart are the boats when they reach their destinations?

Answer 1

This is a Law of Cosines problem. If you sketch a picture of the situation, you will observe that the triangle that is formed has a side angle side relationship. Specifically you know the lengths of two sides of the triangle formed and the angle between the two sides and we are asked to find the third side, the side opposite to the angle.

Thus we are given that a = 19, b = 11, and C = 70° and we are asked to find side c.

The Law of Cosines states that:

c² = a² + b² - 2ab⋅cos C

c² = 19² + 11² - 2(19)(11)cos(70°)

c² = 482 - 418 cos(70°)

c² = 339.03558008987045

c = 18.4 km

Thus the boats are about 18.4 km apart when they reach their destinations.