Answer
The height of the mountain is 1.295 miles.
Work Step by Step
To solve for the elevation, we need to set up a proportion:
The first equation will be for the small triangle:
tan($9^{o}$) = $\frac{y}{x}$
where y is the elevation of the mountain and x is the distance from the mountain to the first point.
The second equation will be for the larger triangle:
tan($3.5^{o}$) = $\frac{y}{13 + x}$
Solving the system of equations:
x = 8.17 miles
y = 1.295 miles
Therefore, the height of the mountain is 1.295 miles.
