Question

A helicopter hovers at an altitude that is 1000 feet above a mountain of altitude 5210 feet. A second, taller peak is viewed from both the mountaintop and the helicopter. from the helicopter, the angle of depression is 43, and the mountaintop, the angle of depression is 19 degree. how far apart are the mountain peaks? what is the altitude of the taller peak?

Answer 1

Given:

Height of Mountain A = 5210 feet
Distance of Mountain A from a helicopter above the peak = 1000 feet
Angle of depression:
Mountain B to helicopter = 43 degrees
Mountain B to Mountain A = 19 degrees

First, draw an illustration and label the enumerated given values.

Observe that there are two right triangles formed:

From the triangle formed by the helicopter and Mountain B,

let x = total height of mountain B
y = leg of first triangle (helicopter and mountain b)
h = hypotenuse
Use the Pythagorean Theorem:

cos (43) = y / h

From the second triangle formed by mountain b and a,

cos (19) = (1000 + y) / h

solve for h and y

then, solve for the height of Mountain B:

x = 1000 + y + 5210