Question

A marine surveyor uses a rangefinder and a compass to locate a ship and an island in the vicinity of the coast on which she stands. The rangefinder indicates that the island is 353 ft from her position and the ship is 474 ft from her position. Using the​ compass, she finds that the​ ship's azimuth​ (the direction measured as an angle from​ north) is 320 degrees and that of the island is 58 degrees. What is the distance between the ship and the​ island?

Answer 1

distance between the ship and the​ island is 465.72 ft

Explanation:

given data

island = 353 ft

ship = 474 ft

ship's azimuth = 320 degrees

island = 58 degrees

to find out

distance between the ship and the​ island

solution

as per given figure we can see that

AC = 353

AB = 474

we get here angle ABC that is = 360 - 320 = 40 degree

and angle BAC is = 180 - 58 = 122

and now we apply here law sign

so

`(BC)/(sinA) = (AC)/(sinB)` ...........1

put here value and we get

`(BC)/(sin122) = (353)/(sin40)`

BC = 465.72 ft

so distance between the ship and the​ island is 465.72 ft