SOLUTION: A ship is approaching a harbour between a pier and a lighthouse. The distance between the pier and the lighthouse is 4.1 nautical miles. The angle between the lines of sight from t

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Question 1111722: A ship is approaching a harbour between a pier and a lighthouse. The distance between the pier and the lighthouse is 4.1 nautical miles. The angle between the lines of sight from the ship to the pier and the lighthouse is 120°. The lighthouse keeper reports that the ship is 3.5 nautical miles away. Determine the distance between the ship and the pier, to two decimal places.
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Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A ship is approaching a harbour between a pier and a lighthouse.
The distance between the pier and the lighthouse is 4.1 nautical miles.
The angle between the lines of sight from the ship to the pier and the lighthouse is 120°.
The lighthouse keeper reports that the ship is 3.5 nautical miles away.
Determine the distance between the ship and the pier, to two decimal places.
:
Draw this out as a triangle, the pier, the lighthouse and the boat
angle at the boat is 120 degrees, side opposite is 4.1 mi
side opposite the lighthouse is the distance from the boat to the pier
Find the angle P at the pier using the law of sines
3.5%2Fsin%28P%29 = 4.1%2Fsin%28120%29
Cross multiply
4.1*sin(P) = 3.5*sin(120)
sin(P) = 3.031%2F4.1
P = 47.67 degrees
Find the angle at the lighthouse
180 - 120 - 47.67 = 12.331 degrees
Side opposite is the dist between the boat and the pier
d%2Fsin%2812.331%29 = 4.1%2Fsin%28120%29
d = .3156*4.734
d = 1.01 mile from the boat to the pier