Question

A surveyor wishes to determine the height of a mountain. At a given position he measures the angle of elevation to the top as 43.66 degrees. He then moves 1000 feet further from the mountain and measures the angle of elevation to the top as 38.2 degrees. How high is the mountain?

Answer 1

Answer:

4,486.93 ft

Step-by-step explanation:

Let 'h' be the height of the mountain and 'x' be the horizontal distance between the first position measured and the top of the mountain.

Two right triangles can be modeled such that their tangent relationships yield:

$tan(43.66) = \frac{h}{x}\\tan(38.2) = \frac{h}{x+1000}$

Solving the linear system:

$x= \frac{h}{tan(43.66)}\\x = \frac{h}{tan(38.2)} -1000\\\frac{h}{tan(43.66)}=\frac{h}{tan(38.2)} -1000\\1000 = 0.222869*h\\h=4,486.93\ ft$

The mountain is 4,486.93 ft high.