Answer to Question #134976 in Trigonometry for Kevin Santos

Question

The bearing of a lighthouse from ship A is 29°NE and the bearing of that same
lighthouse from ship B is 61°NW. If ship A and ship B are on the east-west line 200 km
apart, how far is ship B from the lighthouse?

Answer 1

y - distance between lighthouse and ship B

$61\degree NW + 29\degree NE = 90\degree WE$

ABC is a right triangle.

$\cos\angle BAC = \dfrac{AB}{AC}$

$\cos(90\degree-61\degree)=\dfrac{y}{200}$

$\cos(29\degree)=\dfrac{y}{200}$

$y=\cos(29\degree)*200$

$y=175$ km

Answer: $175$ km is ship B from the lighthouse.