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Question
The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to
Options
`sqrt(3)` b
`"b"/3`
`"b"/2`
`"b"/sqrt(3)`
Solution
`"b"/2`
Explanation;
Hint:
Let the height of the pole BC be h
AC = b + h
Let CD be x
In the right ∆BCD, tan 30° = `"BC"/"AB"`
`1/sqrt(3)= "h"/x`
x = `sqrt(3)`h ...(1)
In the right ∆ACD, tan 60° = `"AC"/"CD"`
`sqrt(3) = ("b" + "h")/x`
x = `("b" + "h")/sqrt3` ....(2)
From (1) and (2) we get
`sqrt(3)`h = `("b" + "h")/sqrt(3)`
⇒ 3h = b + h
2h = b
⇒ h = `"b"/2`
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