A ship leaves a pier on a bearing of S62degreesE and travels 75 km. It then turns and continues on a bearing of S28degreesW for 68 km. How far is the ship from the pier.
Am i right to form a triangle with my info? Distance- sides, Degrees- angles?
2006-10-25 13:34:46 · 3 answers · asked by ? 1 in Science & Mathematics ➔ Mathematics
Yes, you are right. & even better it is a right triangle.
the distance is
sqrt(75^2+68^2)=sqrt(5625+4624)=sqrt(10249)=101.3 km
2006-10-25 13:39:58 · answer #1 · answered by yupchagee 7 · 16⤊ 0⤋
Yes, you're right to form the triangle. It also helps to translate those bearings into compass headings (N is 0°, E is 90°, S is 180°, W is 270°). The first heading is (180-62) 118°, and the second is (180+28) 208°, so the angle between the 2 sides of the triangle you know is (208-118) 90°. That makes the problem easier by far than law of cosines: it's just Pythagorean Theorem, and the distance from the pier is
d² = 75²+68² = 5625+4624 = 10249
d = 101.23 miles.
The more interesting question when you're out at sea is WHICH DIRECTION is the home pier.
2006-10-25 21:06:44 · answer #2 · answered by Philo 7 · 0⤊ 0⤋
yes... it's a 90 degree triangle with the 68 and 75 as the sides...
2006-10-25 20:39:08 · answer #3 · answered by Anonymous · 0⤊ 0⤋