SOLUTION: I am standing at the trailhead of a mountain trail on level ground. I know from my map that the horizontal distance from this spot to the top of the mountain is 3 miles. I find tha

Algebra ->  Trigonometry-basics -> SOLUTION: I am standing at the trailhead of a mountain trail on level ground. I know from my map that the horizontal distance from this spot to the top of the mountain is 3 miles. I find tha      Log On


   

Question 299279: I am standing at the trailhead of a mountain trail on level ground. I know from my map that the horizontal distance from this spot to the top of the mountain is 3 miles. I find that the angle of elevation to the top of the mountain from this point is 4 degrees. What is the height of the mountain, in feet?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can use the Tangent function to find the height of the mountain.
Let h = height of mountain and the horozontal distance to the mountain of 3 miles is the same as the length of the base of the right triangle.
The tangent of the angle of elevation is expressed by h%2F3
, so...
Tan%284%29+=+h%2F3 Solve for h.
h+=+3%2Atan%284%29
h+=+0.20978Miles.
Convert to feet by multiplying by 5,280 ft/mi.
h+=+1107.64feet.