Due in 1 hours, 24 minutes. due fri 06/28/2019 11: 59 p a survey team is trying to estimate the height of a mountain above a level plain. from one point on the plain, they observe that the angle of elevation to the top of the mountain is 24°. from a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 26 how high (in feet) is the mountain? preview

Height of the mountain is 5108.80 feet.

Step-by-step explanation:

From the figure attached, h is the height of a mountain AB.

At a point C angle of elevation of the mountain is 24°

Now survey team gets closer to the mountain by 1000 feet then angle of elevation is 26°.

Now from ΔABC,

tan24 =

0.445 =

h = 0.445(x + 1000)------(1)

From ΔABD,

tan26 =

0.4877 =

h = 0.4877x -----(2)

Now we equation 1 and equation 2

0.4452(x + 1000) = 0.4877x

0.4877x - 0.4452x = 1000(0.4452)

0.0425x = 445.20

x =

x = 10475.29 feet

Now we plug in the value of x in equation 2.

h = (10475.29)×(0.4877)

h = 5108.80 feet

Therefore, height of the mountain is 5108.80 feet