Law of Sine and Law of Cosine

Question

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 1.6 km apart, to be 21° and 48°, as shown in the figure below. Find the distance of the plane from point A and the elevation of the plane. (Round your answers to one decimal place.) 

G=airplane

G to A is the straight highway

2=21°

2+1=48°

Find

distance from the plane to point A   in km

elevation of the plane in km

Answer 1

Draw and label a diagram.

a represents altitude of plane

d represents distance between A and point below plane

Assuming A is closer to the plane than B

tan 42° = d / a, a tan 42° = d

tan 69° = (d + 1.6) / a, a tan 69° = d + 1.6, a tan 69° - 1.6 = d

Set two equations equal and solve for a.

Substitute value of a into

a / h = cos 42° and solve for h