Two Coast Gaurd lookouts, A and B, are on an east-west line, 21 kilometers apart. The bearing of a ship from lookout A is N45°W and it's bearing from lookout B is 60°. How far is the ship from lookout B?
I've been struggling with this problem for almost an hour now. I really have no idea how I'm supposed to solve it. Please help.
Pre-Calc: Bearing Lookout Problem?
2018-03-12 12:19 pm
回答 (2)
2018-03-12 2:11 pm
✔ 最佳答案
Refer to the diagram below, where point S is the ship.In ΔABS :
∠A = 90° - 45° = 45°
∠B = 90° - 60° = 30°
∠S = 180° - (45° + 30°) = 105°
BS / sinA = AB / sinS …. (sine law)
BS / sin45° = (21 km) / sin105°
BS = 21 × (sin45° / sin105°) km
BS = 15.4 km
Distance between the ship and lookout B = 15.4 km.
2018-03-12 12:27 pm
I am taking the 60° bearing from B to be the azimuth. Let S be the ship's location. Draw a sketch of ∆ABS.
∠A = 45°
∠B = 30°
AB = 21 km
Use the angle sum to find ∠S. You will then have all three angles and one side. Apply the sine rule to find side BS. The sine rule can return ambiguous results for an angle, but there is no problem when you are deriving a side.
∠A = 45°
∠B = 30°
AB = 21 km
Use the angle sum to find ∠S. You will then have all three angles and one side. Apply the sine rule to find side BS. The sine rule can return ambiguous results for an angle, but there is no problem when you are deriving a side.
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