Asked by T
A power failure on the bridge of a Great Lakes freighter has resulted in the ship's navigator having to do her own calculations. She measures the angle between the ship's course and a lighthouse on shore as 32°. After the ship has travelled 1500 m, she measures the angle to be 72°. Determine if the ship was closer to or farther from the lighthouse at the second sighting, and by what distance.
How should this triangle look?
How should this triangle look?
Answers
Answered by
Steve
draw a vertical line -- that's the ship's course
at the bottom (A) draw a line at an angle of 32° to a point L (lighthouse)
some distance up the line at point B, draw another line to L, this time at an angle of 72°
(no, it doesn't have to be exact.)
Now you have <BAL=32°, <ABL=108°, and AB=1500
You know that the ship is closer, since its closest approach would be when BL is perpendicular to AB, and angle B is closer to ┴ than angle A.
Anyway, you now know that <L=40°, so using the law of sines,
BL/sin32° = AL/sin108° = 1500/sin40°
at the bottom (A) draw a line at an angle of 32° to a point L (lighthouse)
some distance up the line at point B, draw another line to L, this time at an angle of 72°
(no, it doesn't have to be exact.)
Now you have <BAL=32°, <ABL=108°, and AB=1500
You know that the ship is closer, since its closest approach would be when BL is perpendicular to AB, and angle B is closer to ┴ than angle A.
Anyway, you now know that <L=40°, so using the law of sines,
BL/sin32° = AL/sin108° = 1500/sin40°
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