Question

Two ships leave a harbor entrance at the same time. The first ship is traveling at a constant 16 miles per hour, while the second is traveling at a constant 18 miles per hour. If the angle between their courses is 146°, how far apart are they after 2 hours? (Round your answer to the nearest whole number.)

Answer 1

The first ship is traveling at a constant 16 miles per hour, while the second is traveling at a constant 18 miles per hour. If the angle between their courses is 146°, how far apart are they after 2 hours

law of cosines.

one side of the triangle= 16 mph x 2 hours = 32 miles
utter side of the triangle = 18 mph x 2 hours = 36 miles
angle between the = 146 degrees

law of cosines

a^2 = b^2 + c^2 - 2bc cos( α )

a^2 = 32^2 + 36^2 - 2 x 32 x 36x cos (146)

a^2 = 2126.55

a=46.11mi--------answer