Power failure Question

Question

1. 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. (4 marks)

Answer 1

32 degrees, then 72 degrees after moving 1500 meters

construct two right triangles, with distances to the lighthouse as the hypotenuses

base = 1500 for the larger right triangle. the smaller right triangle has a smaller hyptenuse, which means

the ship is closer after moving 1500 meters

distance originally to the lighthouse = 1500/sin58= 1768.7676 meters using Law of Sines

upper angle is 90-32= 58. hypotenuse is the side opposite the 90 degree angle. Sin90=1

H/Sin90 = 1500/sin58

H/1 = 1500/sin58= 1500/.848 = about 1769 meters

distance later after moving 1500 = 1769sin32/sin108

Use Law of Sines again, on the non-right triangle adjoining the smaller right triangle.

It definitely helps to draw a diagram

largest angle of the non-right triangle is 180-72 = 108 degrees. It's opposite the side of length 1769

1769/sin108 = h/sin32 where h=hypotenuse of the smaller right triangle

h= sin32(1769)/sin108= about 986

it moved closer to the lighthouse by 1769 - 986 = 783 feet

(no guarantees on the above arithmetic calculations, but that's the basic method)

Answer 2

You get a triangle that is 32°, 180-72 = 108°, and 40° at the LH. You are given that the side opposite the 40° is 1500 meters. You are trying to find the side opposite to the angle of 32° (distance to LH from boat) Use law of sines: x/sin(32) = 1500/sin(40) to solve for x

Please consider a tutor. Take care.