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:
[tex]tan(43.66) = \frac{h}{x}\\tan(38.2) = \frac{h}{x+1000}[/tex]
Solving the linear system:
[tex]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[/tex]
The mountain is 4,486.93 ft high.
