Trigonometry airplane descent

Question

1. An airplane traveling 400 mph at a cruising altitude of 5.8 mi begins its descent. If the angle of descent is 4° from the horizontal, determine the new altitude after 15 min. Round to the nearest tenth of a mile.

Answer 1

let h be the vertical distance traveled by airplane.

distance traveled by plane: 400*(15/60) or 100 miles. 15 miles is 1/4 of an hour.

h/100=sin(-4 degrees)

h=100*sin(-4 degrees) or -7.0 miles

The new altitude will be 5.8 + -7.0 or -1.2 miles.