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 18 degree. how far apart are the mountain peaks? what is the altitude of the taller peak?

Answer 1

the altitude of the taller peak is equal to 5468.4 ft

Explanation:

given,

altitude of the helicopter = 1000 ft

height of the mountain = 5210 ft

Angle of depression from helicopter = 43°

Angle of depression from mountain = 18°

`tan 18 = (h)/(s)`

`tan 43 = (1000-h)/(s)`

`(h)/(tan 18) = (1000-h)/(tan 43 )`

2.87 h = 1000 - h

3.87 h = 1000

h = 258.4 ft

Taller peak =

= 5210+258.4

= 5468.4 ft

the altitude of the taller peak is equal to 5468.4 ft

Answer 2

x - horizontal distance from peak to peak
y – difference between the altitudes of two peaks

Equations:
y/x = tan(17°)
(1100 – y)/x = tan(46°)

Solution:
y = (1100 tan(17°)) / (tan(17°) + tan(46°)) = 250.74 ft
x = y / tan(17°) = 820.12 ft

Horizontal distance from peak to peak is 820 ft.
Altitude of the taller peak is 5300 + 250 = 5550 ft.

The direct distance from peak to peak is √(x²+y²) = 857.6 ft.