Posted by subhradeep on .
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.
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.