how to solve this word problem?

Question

two people, Bert and Alain, 8.4 miles apart spot a hot air balloon at the same time. the angle of elevation from Bert to the balloon is 24 degrees 10'. The angle of elevation from Alain to the balloon is 47 degrees 40'. The balloon is between the two. What is the balloon's altitude?

Answer 1

Here is one way of solving this problem...it may not be the way you were expected to solve it.

Darw a figure!

Assume Bert is standing at the origin (0,0). The line of elevation has the equation y = x tan 24 degree 10'.

Alain is standing at the point (8.4,0) and the equation for his line of elevation is

y = (x - 8.4) tan 47 degrees 40'.

If you set these two expressions for y = to each other and solve for x, you will have the abscissa of the perpendicular from the balloon to the ground.

Plug the value of x into Bert's equation and you will have the altitude of the balloon.