Question 1142029
your diagram looks like this.


<img src = "http://theo.x10hosting.com/2019/060903.jpg" alt="$$$" >


P and Q are both 5200 meters above sea level.


triangles PMQ and PMB are formed.


angle MPQ is 15 degrees.


angle MQB is 35 degrees.


the height of MB is equal to x.


the length of QB is equal to y.


tan(15) = x / (4000 + y)


tan(35) = x / y


solve for x in both equations to get:


x = (4000 + y) * tan(15)


x = y * tan(35)


replace x in the first equation with y * tan(35) to get:


y * tan(35) = (4000 + y) * tan(15)


simplify to get y * tan(35) = 4000 * tan(15) + y * tan(15)


subtract y * tan(15) from both sides of the equation to get:


y * tan(35) - y * tan(15) = 4000 * tan(15)


factor out the y to get y * (tan(35) - tan(15)) = 4000 * tan(15)


divide both sides of the equation by tan(35) - tan(15) to get:


y = 4000 * tan(15) / (tan(35) - tan(15))


solve for y to get y = 2479.528227 meters.


in triangle QMX, solve for x to get x = 2479.528227 * tan(35) = 1736.184356 meters.


the height of the mountain is x + 5200 = 6936.184356 meters.