Question

Two submarines, one cruising at 25 knots and the other at 20 knots, left a naval base at the same moment. Three hours later, they were 100 nautical miles apart. What was the measure of the angle between their courses?

Answer 1

The correct answer is 95°

Answer 2

Measure of the angle between their courses is 95°

Explanation:

Speed of submarine 1 = 25 knots = 28.77 mph

Speed of submarine 2 = 20 knots = 23 mph

Time taken = 3 hours

Distance traveled by submarine 1 = 28.77 x 3 = 86.31 miles

Distance traveled by submarine 2 = 23 x 3 = 69 miles

Distance between them is 100 nautical miles = 115.08 miles

Refer the figure

By cosine formula we have

`cosB=(a^2+c^2-b^2)/(2ac)`

a = 86.31 miles

b = 115.08 miles

c = 69 miles

Substituting

`cosB=(86.31^2+69^2-115.08^2)/(2* 86.31* 69)\\\\cosB=-0.0867\\\\B=94.98^0=95^0`

Measure of the angle between their courses is 95°