Question

A ship is 15 miles due west of lighthouse A on the island of Hawaii. If lighthouse B is 6.2 miles due south of lighthouse A, what is the bearing to the nearest tenth of a degree of the ship from lighthouse B? To the nearest tenth of a mile, how far is the ship from lighthouse B?

Answer 1

i think its 6.2 miles

Answer 2

67.5°

16.2 miles

Explanation:

According to data, ship is at 15 miles due west to light house A.

Light house B is 6.2 miles due south of Light house A

Now,

Ship______15 miles_____Light house A

║

║ 6.2 miles

║

Light house B

You can see that, if you draw an imaginary straight line from light house B to ship, it is forming a right angle triangle,

so, according to Pythagoras theorem,

(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2

We need to find hypotenuse,

Base = 6.2, Perpendicular = 15

So, H^2 = (15)^2 + (6.2)^2

H^2 = 225 + 38.44

H = 16.23 miles

now for rounding of to nearest 10th place

H = 16.2 miles

Now for angle of Ship from light house is

Cos^Ф = Base/Hypotenuse

Base = 6.2

Hypotenuse = 16.2

Cos^Ф = 6.2/16.2

Ф = 67.49°

After rounding off to the nearest tenth place

Ф = 67.5°