Question

A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 38°. The distance between the Gladstone and the Norman is 2640 yards. The Norman measures an angle of 57° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager?

Answer 1

The distance between the Norman and the Voyager is 1,632 yards

Explanation:

Let

C -----> the measure of the angle between the Norman and the Gladstone

c ------> the distance between the Norman and the Gladstone

a ----> the distance between the Norman and the Voyager

A----> the measure of the angle between the Norman and the Voyager

step 1

Find the measure of angle C

Remember that the sum of the interior angles of a triangle must be equal to 180 degrees

so

38°+57°+C=180°

95°+C=180°

C=180°-95°=85°

step 2

Find the distance between the Norman and the Voyager

Applying the law of sines

c/sin(C)=a/sin(A)

we have

C=85°

A=38°

c=2,640 yd

substitute and solve for a

2,640/sin(85°)=a/sin(38°)

a=2,640(sin(38°))/sin(85°)

a=1,632 yd