Question

angle of elevation of the top of a mountain to a man is 45degree.if we walk along a slope of 30 degree of the mountain 100 meters then the angle of elevation of the top of mountain becomes 60 degree.find the height of the mountain.

Answer 1

The line of sight of 45 deg angle is
drawn as the hyp. of a rt triangle.
The ht. of the mountain is the ver. side of the triangle. the hor. side
side = 100 + X. The line of sight of the 60 deg. angle represents the hyp.
of a 2nd triangle and the ht. of the
mountain is the ver. side of both triangles.

Tan(45) = h /(100+X),
h = (100 + X) * Tan(45),
.
Tan(60) = h / X,
h = x * Tan(60).

h = (100 + X) * Tan(45) = X * Tan(60),
Solve for X:
70.7 + 0.707X = 1.73X,
- 1.73X + 0.707X = - 70.7
X = 69 METERS.
h = 69 * TAN(60) = 119.5 Meters =
ht. of mountain.