Question 999146
The height of the hill is x feet above the hiker.
The tangent of the height is x/the distance the hiker is from the perpendicular.  
tan 22=0.4040=x/distance(d)
700 feet closer, the angle is now 38 degrees.
The height hasn't changed, but the distance is less
tan 38=0.7813=x/(d-700)
0.7813*(d-700)=0.4040d , because both of these tangents are equal to the same x or height, so they are equal to each other.
0.7813d-546.90=0.404d
0.3773d=546.90
d=1449.51 ft.  THAT IS NOT THE HEIGHT, ONLY THE LENGTH OF THE ADJACENT SIDE.
TAN 22=X/1449.51
1449.51*0.404=585.60 FEET
check with the other
749.51*0.7813=585.58 FEET, the same given rounding error.