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

Answer:

Height of the mountain was 28331.8 feet.

Step-by-step 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 = $\frac{h}{x}$

x = $\frac{h}{tan85}$ -----(1)

Similarly, from ΔABD,

tan83 = $\frac{h}{(x+1000)}$

x + 1000 = $\frac{h}{tan83}$

x = $\frac{h}{tan83}-1000$ -----(2)

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

$\frac{h}{tan85}=\frac{h}{tan83}-1000$

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.