At 12 noon a ship observes a lighthouse at a distance of 15 km in a direction of N50°E. It sails at 15 km/h in a direction S35°W. How do you find the distance and direction of the lighthouse from the ship at 3 pm?

1 Answer
Nghi N.
Sep 19, 2015

Find distance from boat to lighthouse

Explanation:

Call A the boat, B the lighthouse, and C the new position of the boat.
We have: AB = 15 ; AC = 15 km x 3 hrs = 45
Angle A = (180 - 50) + 35 = 165 deg.
To find the side BC, apply the trig identity:
a^2 = b^2 + c^2 - 2bc.cos Aa2=b2+c2−2bc.cosA
a^2 = (15)^2 + (45)^2 - 2(45)(15).cos 165 =a2=(15)2+(45)2−2(45)(15).cos165=
a^2 = 225 + 2025 - 1350(-0.97) = 3559.5a2=225+2025−1350(−0.97)=3559.5

a = BC =59.66a=BC=59.66 Km

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