math
posted by subhradeep .
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.
Respond to this Question
Similar Questions

precal
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is . From a point 1500 feet closer to the mountain along … 
math
if someone could please help that would be muchly appreciated. A group of mountain climbers are using trigonometry to find the height of a mountain located in the rockies. From point A, which is due west of the mountain, the angle … 
trig confused.. pls help
A group of mountain climbers are using trigonometry to find the height of a mountain located in the Rockies. From point A, which is due west of the mountain, the angle of elevation to the top is 56 degrees. From point B, which is due … 
PreCal
Angel of Elevation: You are skiing down a mountain with a vertical height of 1500 feet. The distance from the top of the mountain to the base is 3000 feet. What is the angle of elevation from the base to the top of the mountain? 
trig
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 24. From a point 1000 feet closer to the mountain … 
angles
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 25 degrees. From a point 1225 feet closer to the … 
Trigonometry
At a point on a level ground, the angle of elevationof a mountain top B is 42deg36min. At a pointD350 meters nearer the mountain, the angle of elevation is 51deg 43 min. Find the height of the mountain? 
Math
a surveyor is 3 miles from a mountain. The angle of elevation from the ground to the top of the mountain is 15 degrees. What is the height of the mountain? 
math
A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 27∘. From a point 1000 feet closer to the mountain … 
Maths
Say I'm at an unknown distance from a mountain, called point P, and I estimate the angle of elevation to the top of the mountain is 13.5 degrees. Then I move to point N, which is 100 meters closer to the mountain, and I estimate the …