Being some distance from a mountain a man looks up at a 9 degree angle to see the top of the moutain. he then moves 13 miles away from the mountains at looks up at a 3.5 degree angle to see the top of the mountain. How tall is the mountain?

Answer 1

Calculus? This is a standard trig question.

draw the figure, two right triangles.

inner triangle: tan9=h/x x is the distance to the mountan.
outer triangle: tan3.5=h/(x+13)

two equations, two unknowns.
x=h/tan9

x=h/tan3.5 -13
h/tan9=h/tan3.5 - 13
solve for h