Posted by **subhradeep** on Sunday, August 8, 2010 at 4:58am.

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.

- math -
**Henry**, Tuesday, August 10, 2010 at 9:17pm
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.

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