Question

Select the correct answer.

A cruise ship leaves its port at a heading of 135°. It travels for 400 miles, then turns to a heading of 180°. After another 250 miles, it reaches an
Island
What is the approximate distance between the port and the island?
A. 284.7 miles
B. 471.7 miles
C. 603.3 miles
D. 541.5 miles

Answer 1

`{\text{C. }603.3\:\mathrm{miles}`

Explanation:

The Law of Cosines works for any triangle and can be used to solve a triangle when we are given two sides and the angle between them.

Letting the missing side be
`c`:

`c^2=a^2+b^2-2ab\cos C,\\c^2=400^2+250^2-2\cdot 400\cdot 250\cdot \cos135^(\circ),\\c^2=363921.356237,\\c=603.258946256\approx \boxed{\text{C. }603.3\:\mathrm{miles}}`