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प्रश्न
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.
उत्तर
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
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