Aship 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?

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

Step-by-step 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