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.

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°:

[tex]tan(x) = 3/4[/tex]

[tex]height / d = 3/4[/tex]

[tex]d = (4/3)*height[/tex]

angle of elevation y°:

[tex]tan(y) = 5/7[/tex]

[tex]height / (d+150) = 5/7[/tex]

[tex]7*height = (d+150) * 5[/tex]

[tex]7*height = 5d+750[/tex]

[tex]7*height = (20*height/3)+750[/tex]

[tex]21*height = 20*height+2250[/tex]

[tex]height = 2250\ meters[/tex]

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.​

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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.