# trigonometry

posted by .

a surveyor finds that from Point A on the ground the angle of elevation to the top of a mountin is 23 degrees. when he is at point B that is 1/4 closer to the base of the mountain the angle of elevation is 43 degrees. how high is the moutnain? One mile =5280 feet. (Assume that thr base of the mountain and the two observation points are on the same line.)Give answer to the nearest foot.

• trigonometry -

tan23 = Y/X,
Y = Xtan23,

tan43 = Y/(X-.25).
Y = (X-0.25)tan43.

y = Xtan23 = (X-0.25)tan43,
Xtan23 = (X-0.25)tan43,
Xtan23 = Xtan43-0.25tan43,
0.4245X = 0.9325X-0.2331,
0.4245X-0.9325X = -0.2331,
-0.508X = -0.2331,
X = 0.4589 Miles.

y = 0.4589tan23 = 0.1948 miles.

Y = 0.1948mi * 5280ft/mi = 1029 Ft.
= Height of mountain.

## Similar Questions

1. ### math trigonometry

From on point on the ground the angle of elevation to the peak of a mountain is 10.38 degrees and from another pont 15,560 feet closer to the mountain, the anle of elevation is 14.67 degrees. Both point are due south of the mountain. …
2. ### Precalculus

From a point on ground level, you measure the angle of elevation to the top of a moutain to be 38 degrees. Then you walk 200 m fartheraway from the mountain and find that the angle of elevation is now 20 degrees. Find the height of …
3. ### trigonometry

The angle of elevation of the top of a tower to point A on the ground is 61 degrees. At point B it is 600 feet farther from the base, in line with the base and the first point and in the same plane, the angle of elevation is 32 degrees. …
4. ### math

if someone could please help that would be muchly appreciated. A group of mountain climbers are using trigonometry to find the height of a mountain located in the rockies. From point A, which is due west of the mountain, the angle …
5. ### trig confused.. pls help

A group of mountain climbers are using trigonometry to find the height of a mountain located in the Rockies. From point A, which is due west of the mountain, the angle of elevation to the top is 56 degrees. From point B, which is due …
6. ### trigonometry

as you walk on a straight level path toward a mountain, the measure of the angle of elevation to the peak from one point is 33 degrees. From a point 1000 feet closer, the angle of elevation is 35 feet. How high is the mountain?
7. ### angles

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 25 degrees. From a point 1225 feet closer to the …
8. ### geometry

a surveyor on level ground finds the angle of elevation of a 138-foot flagpole to be 47 degrees how far from the base of the pole is the surveyor?
9. ### Math

a surveyor is 3 miles from a mountain. The angle of elevation from the ground to the top of the mountain is 15 degrees. What is the height of the mountain?
10. ### Maths

Say I'm at an unknown distance from a mountain, called point P, and I estimate the angle of elevation to the top of the mountain is 13.5 degrees. Then I move to point N, which is 100 meters closer to the mountain, and I estimate the …

More Similar Questions

Post a New Question