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ABCD is a square plot. The angle of elevation of the top of a pole standing at D from A or C is 30° and that from B is Θ then Tan Θ equal to ?
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- √6
- 1/√6
- √3/√2
- √2/√3
- a√2
Correct Option: B
Let a be the length of a side of square plot ABCD and h, the height of the pole standing at D. Since elevations of P from A or C is 30° and that from B is Θ,
∴ In triangle Δ PCD, tan 30° = h/a
i.e h/a = 1/√3 .............. (1)
And in triangle Δ PBD,
Since PD = h and BD = √(AB2 + AD)2 = a√2.
Put the value of PD and BD , we will get
tan Θ = PD/BD = h/(a√2)
put the value of h/a from equation (1)
tan Θ = 1/√2 x 1/√3
tan Θ = 1/√6
