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 along the plain, they find that the angle of elevation is 27.

Question

How high (in feet) is the mountain?

Answer 1

Make a sideview sketch
you should have 2 triangles, one right-angled containing the height and a scalene triangle with angles 24° , 153° (the supplement of 27°) and 3°
the side opposite the 3° angle is 1000
by let the side opposite the 24° be x, (also the hypotenuse of the right-angled triangle)

x/sin24 = 1000/sin3
x = 1000sin24/sin3

let the height of the mountain be h
sin 27 = h/x
h = x sin27 = (1000sin24/sin3)(sin27)
= 3528.25

Answer 2

what....the......heck...is....trig..........

Answer 3

d = hor. distance from foot of mountain to point where 24 deg. is measured.
Tan24 = h/d, h = d*Tan24.
Tan27 = h/(d-1000), h = (d-1000)Tan27.

d*Tan24 = (d-1000)*Tan27,
d = (d-1000)*1.11,
0.9d = d-1000,
d = 10,000 Ft.
h = d*Tan24 = 4,450 Ft.

Answer 4

Howdy everyone, here's the equation you need for this:
tan 24 = h/((h/(tan 27)) + 1000)

Just plug your numbers into that equation and you'll have the right answer.