Question

A ship travels due east from Bar Harbor 38 miles before turning north. The ship's engine cuts out after a while and immediately radios for help. The navigator of the rescue boat determines that the shortest route from Bar Harbor to the ship is 72 miles long. From this information, is it possible for you to calculate the exact direction the rescue boat must travel from shore to intercept the stranded boat? Explain why or why not.

Answer 1

Answer:

Explained

Explanation:

Given:

Ship travels due east from the Bar Harbor 38 miles before turning north

Yes it possible to calculate the exact direction of the ship by assuming there are no large islands in the way, and that the isolated ship does not cut off very far, then what we have here is a right triangle with a 72-mile as hypotenuse and a 38-mile as  "adjacent" side. If θ is the angle out of Bar Harbor, we can write

$cos\theta = \frac{38}{72} = 0.52778$, and θ = 58.14457°, or 58° 8' 40" north of east. That will be  the exact direction.