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°
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?
1 answer
1 answer