Question

A plane flies 1.2 hours at 120 mph on a bearing of

20°. It then turns and flies 3.3 hours at the same
speed on a bearing of 110°. How far is the plane from
its starting point?

Answer 1

9514 1404 393

Answer:

421.4 miles

Explanation:

The flight legs are orthogonal, so the distance can be found using the Pythagorean theorem:

1.2 h × 120 mph = 144 mi

3.3 h × 120 mph = 396 mi

The distance at the end of the second flight leg is ...

d = √(144² +396²) = √177552 ≈ 421.37

The plane is about 421.4 miles from its starting point.

_____

The heading to its end point is 20° +arctan(3.3/1.2) ≈ 90.02°.