Two ocean liners leave from the same port in Puerto Rico at 10:00 a. m. One travels at a bearing of N 51o W at 14 miles per hour, and the other travels at a bearing of S 56o W at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places ...?

We find the components of each liner's speed in the North direction and the West direction.

First liner:

North component = 14sin (51)

= 10.9 mph

Northward distance covered:

10.9 x 2

= 21.8 miles

West component = 14cos (51)

= 8.8 mph

Westward distance covered:

17.6 miles

Second liner:

North component = - 17sin (56)

= - 14.1 mph

Northward distance (negative sign because direction opposite to North):

-14.1 x 2

= - 28.2 miles

West component = 17cos (56)

= 9.5 mph

Westward distance:

9.5 x 2

= 19 miles

Distance = √[ (x₂ - x₁) ² + (y₂ - y₁) ²]

= √ (-28.2 - 21.8) ² + (19 - 17.6) ²

= 50 miles