Pre-Calculus homework help.?

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

Make two triangles. In both, the height of the mountain is the opposite side. The angle of elevation is the adjacent angle. The adjacent sides are x and x-2000.

sin 31 = height / x or height = x sin 31
sin 36 = height / x-2000 or height = (x-2000) sin 36

x sin 31 = (x-2000) sin 36
x / (x-2000) = sin 36 / sin 31
x / (x-2000) = 1.14
x = 1.14(x-2000)
x = 1.14x - 2282.5
-.14 x = -2282.5
x = 16303

height = x sin 31
height = 16303 sin 31
height = 8397 ft.

Answer 2

The best thing you have to do is draw a picture of the situation. This is a picture of a right triangle. The height is what you are trying to find and the angle 31 degrees is the angle opposite to the height. But you do not have the length of the hypotenuse nor the length of the leg to do pythagorean. This just means you have to do trig functions. The angle 36 degrees is made when you move further into the triangle. (so your picture would have a triangle inside a triangle) Remember that the mountain stays the same height no matter what angle of elevation it is. So a wise thing to do is label your picture and your angles. Remember a triangle has 180 degrees and that you are dealing with a right triangle. Remember a straight line also equals 180 degrees. These will help you get an unknown angles. When you have all of your angles you can just do trig functions SOH CAH TOA. I suggest you first find the length of the hypotenuse by (2000 sin 144) / sin 5. Then after you have that then you can use (length of hypotenuse)sin 31 = h. h is your height. When i calculated i got 6946.9 feet.