# Thread: Law of Sines Application Help

1. ## Law of Sines Application Help

A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 5 mi. apart, to be 32 degrees and 48 degrees as shown in the figure.
a) Find the distance of the plane from point A.
b) Find the elevation of the plane.

imgur: the simple image sharer

Obviously the large angle of the triangle is 100 degrees. I've tried sketching right triangles here and there but can't get an accurate distance because it isn't directly in the middle of the 5 mi. gap.
So how do I go about solving this using the Law of Sines? Help please Thanks in advance.

2. ## Re: Law of Sines Application Help

I don't know how to say this differently: you need to find the angles of the triangle and then apply the law of sines.

3. ## Re: Law of Sines Application Help

Okay it just kind of hit me. Sketch two right triangles on either side. That leaves one angle that will add with the other on the ground for 90 degrees? Seems like that's what you meant. Otherwise, I thought I remembered a Geometry rule about angles in parallel lines that are oriented like those on the outsides equaling a total. Supplementary? I'm going to work out the first way, thank you.

4. ## Re: Law of Sines Application Help

Originally Posted by Acoustic95
I remembered a Geometry rule about angles in parallel lines that are oriented like those on the outsides equaling a total. Supplementary?
Yes, the angle marked 32 degrees and angle A in the triangle are alternate interior angles and are therefore equal.

5. ## Re: Law of Sines Application Help

I appreciate your help I think I have this one whipped now.

6. ## Re: Law of Sines Application Help

Angle PBA=48. By the sine rule AP/sin48=5/sin100
When you ask for the elevation of the plane you need to say where from. It is 32 from A and 48 from B.