Question

From a point on the ground the angle of elevation of the top of a tower is x°. Moving 150 meters away from that point the angle of elevation was found to be y° .If tan x=3/4 and tan y=5/7 find the height of the tower.​

Answer 1

Answer:

The height of the tower is 2250 meters

Step-by-step explanation:

let's say that when the angle of elevation is x°, the distance to the base of the tower is 'd'. So when the angle of elevation is y°, the distance is d+150.

The tangent of the angle of elevation is the height of the tower (opposite side) over the horizontal distance to the tower (adjacent side).

Then we have that:

angle of elevation x°:

$tan(x) = 3/4$

$height / d = 3/4$

$d = (4/3)*height$

angle of elevation y°:

$tan(y) = 5/7$

$height / (d+150) = 5/7$

$7*height = (d+150) * 5$

$7*height = 5d+750$

$7*height = (20*height/3)+750$

$21*height = 20*height+2250$

$height = 2250\ meters$