A problem for my Pre-Calc homework.?

Question

A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 31 degrees. From a point 2000 feet closer to the mountain along the plain, they find that the angle of elevation is 36 degrees.

How high is the mountain in feet?

Thanks in advance.

Answer 1

Let x be the intitial distance from the mountain and y be the height of the mountain. Therefore, tan(31)=y/x=.6.
But when the observer gets 2000 feet closer, the angle of elevation becomes 36 degrees: tan(36)=y/(x-2000)=.726.
Taken together these two equations imply that y=.6x and y=.726*(x-2000). To solve just set these two equation equal: .6x=.726(x-2000)....-.126x=-1452......x=11523.8 feet.

Answer 2

If you draw a figure of the problem, you'll notice that there are two right triangles that overlap, both of which have as the vertical side the height of the mountain.

For the large triangle with the 31 degree angle of elevation, label the horizontal base as x. For the smaller triangle with the 36 degree angle of elevation, label the horizontal base x - 2000.

For both triangles, label the height of the mountain y.

Since you're dealing with an opposite side and an adjacent side, you'll use tangent to solve it.

tan 31 = y/x
tan 36 = y/(x - 2000)

Solve both equations for y, and set the two expressions with x in them equal to each other. Then you can find x and substitute to find y.

Answer 3

I don't have trig tables, but heres how
If height =h, initial distance away = x
then
h/x =tan 31
h/x-2000 = tan 36
This gives you two simple simultaneos equations to solve