MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

Answer: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 = [tex]\frac{h}{x+1000}[/tex]0.445 = [tex]\frac{h}{x+1000}[/tex]h = 0.445(x + 1000)------(1)From ΔABD,tan26 = [tex]\frac{h}{x}[/tex]0.4877 = [tex]\frac{h}{x}[/tex]h = 0.4877x -----(2)Now we equation 1 and equation 20.4452(x + 1000) = 0.4877x 0.4877x - 0.4452x = 1000(0.4452)0.0425x = 445.20x = [tex]\frac{445.20}{0.0425}[/tex]x = 10475.29 feetNow we plug in the value of x in equation 2.h = (10475.29)×(0.4877)h = 5108.80 feetTherefore, height of the mountain is 5108.80 feet