Question 1198061
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This is one way to do the drawing
<img src = "https://i.imgur.com/LUxuhwp.png">
The observation points are at B and C. 
The mountain is represented by segment FD, which has a height of h+2.


Segments:
AB = x
BC = 900
FA = h
AD = CE = 2
FD = h+2


Angles:
angle ABF = 47 degrees
angle ACF = 35 degrees


Let
u = tan(47)
v = tan(35)
which will help us do the symbolic operations shown below a bit easier.


Focus on triangle ABF.
Use the tangent ratio to say
tan(angle) = opposite/adjacent
tan(B) = FA/AB
tan(47) = h/x
u = h/x
ux = h
h = ux


Now focus on triangle ACF
tan(C) = FA/AC
tan(35) = h/(x+900)
v = h/(x+900)
v(x+900) = h
vx + 900v = h
vx + 900v = ux
900v = ux - vx
900v = (u-v)x
x = 900v/(u-v)


Therefore,
h = ux
h = u*900v/(u-v)
h = 900uv/(u-v)
we have this fairly tidy formula to calculate the height based on the tangents of the angles mentioned, and also based on the distance between the observation points from B to C.


Now plug in the definitions for u and v mentioned earlier
h = 900uv/(u-v)
h = 900*tan(47)*tan(35)/(tan(47)-tan(35))
h = 1815.86000966682


which leads to:
h+2 = 1815.86000966682+2 = 1817.86000966681


When rounding to the nearest whole number we get <font color=red>1818 meters</font> as the final answer.


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