A jetliner flies east for 563.0 km, then turns 30.0° toward the south and flies another 348.0 km

A jetliner flies east for 563.0 km, then turns 30.0° toward the south and flies another 348.0 km.

(a) How far is the plane from its starting point?

(b) In what direction could the jetliner have flown directly to the same destination (in a straight-line path)?

(c) If the jetliner flew at a constant speed of 397.0 km/h, how long did the trip take?

(d) Moving at the same speed, how long would the direct flight have taken?

Horizontal(east) = 563 + 348 cos 30 = 864.38 km
Vertical(south) = 348 sin 30 = 174 km

Drawing the right angled triangle will help

Distance from starting point = square root(864.38^2 + 174^2) = 881.72 km

Direction = tan^-1 (174/864.38) = 11.38 deg to the south

Distance of path taken = 563 + 348 = 911 km

Time taken for trip = 911/397 = 2.29 hours or 2 hours 17 min

Time taken for direct flight = 881.72/397 = 2.22 hours or 2 hours 13min