Question

Batman is trying to find Aquaman because the because the bad guys won't stop being mean. He sails on a boat traveling 85 miles at a heading of LaTeX: N42^\circ EN 42 ∘ E from a port. How far north and how far east is Batman from the port?

Answer 1

• Batman's distance far East is 57 miles.

• Batman's distance far North is 63 miles.

Explanation:

In the diagram, from the port A, he travels to Port B.

• Batman's distance far North is the distance from B to C.

• Batman's distance far East is the distance from A to C.

Using Trigonometric ratios

`sin 48 =(|BC|)/(85) \\|BC|=85 X sin 48\\|BC|=63.17 miles`

Similarly

`cos 48 =(|AC|)/(85) \\|AC|=85 X cos 48\\|AC|=56.88 miles`

Therefore:

• Batman's distance far East is 57 miles.

• Batman's distance far North is 63 miles.