Question

From a window A, 10 m above the ground the angle of elevation of the top C of a tower is x°, where tan `x^circ = 5/2` and the angle of depression of the foot D of the tower is y°, where tan `y^circ = 1/4`. Calculate the height CD of the tower in metres.

Answer 1

Let CD be the height of the tower

And height of window A from the ground = 10 m

In right ΔAEC, we have

`tan x^circ = (CE)/(AE)`

`\implies 5/2 = (CE)/(AE)`   ...`(∵ tan x = 5/2)`

∴ `AE = (2CE)/5`  ...(i)

In right ΔAED, we have

`tan y^circ = (ED)/(AE)`

`\implies 1/4 = 10/(AE)`

∴ AE = 40

Now substituting the value AE in (i), we get

`2/5 CE = 40`

`\implies CE = (40 xx 5)/2 = 100  m`

∴ Required height of tower 

CD = CE + ED

= (100 + 10) m

= 110 m