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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?

Respuesta :

Answer:

  • Batman's distance far East is 57 miles.
  • Batman's distance far North is 63 miles.

Step-by-step 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

[tex]sin 48 =\dfrac{|BC|}{85} \\|BC|=85 X sin 48\\|BC|=63.17 miles[/tex]

Similarly

[tex]cos 48 =\dfrac{|AC|}{85} \\|AC|=85 X cos 48\\|AC|=56.88 miles[/tex]

Therefore:

  • Batman's distance far East is 57 miles.
  • Batman's distance far North is 63 miles.
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