Question

To measure the height of a mountain, a surveyor took two sightings, one 1000 feet farther from the mountain of the other. The first angle of elevation was 85° and the second was 83°.

What is the mountain’s height?

Answer 1

Height of the mountain was 28331.8 feet.

Explanation:

An observer took the measurements from two sights C and D.

Point D was 1000 ft away from the earlier sight point C.

Angle of elevations from points C and D were 85° and 83° respectively.

From ΔABC,

tan85 =
`(h)/(x)`

x =
`(h)/(tan85)` -----(1)

Similarly, from ΔABD,

tan83 =
`(h)/((x+1000))`

x + 1000 =
`(h)/(tan83)`

x =
`(h)/(tan83)-1000` -----(2)

Now we substitute the value of x from equation (1) in the equation (2)

`(h)/(tan85)=(h)/(tan83)-1000`

0.122785h - 0.087488h = 1000

0.035296h = 1000

h = 28331.822 ft

h ≈ 28331.8 ft

Therefore, height of the mountain was 28331.8 feet.