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patrickwilson
01.06.2020 •
Mathematics
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?
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Ответ:
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}](/tpl/images/0673/0604/bd337.png)
x =
-----(1)
Similarly, from ΔABD,
tan83 =![\frac{h}{(x+1000)}](/tpl/images/0673/0604/64d9e.png)
x + 1000 =![\frac{h}{tan83}](/tpl/images/0673/0604/e9ee4.png)
x =
-----(2)
Now we substitute the value of x from equation (1) in the equation (2)
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.
Ответ:
3x^3 - 10x^2 + 40x - 160 R. 635
Step-by-step explanation: