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Question
The topmost branch of a tree is tied with a string attached to a pole in the ground. The length of this string Is 200m and it makes an angle of 45° with the ground. Find the distance of the pole to which the string is tied from the base of the tree.
Solution
The topmost branch of the tree is at point B and C is the point on the ground to which the topmost branch is tied.
In ΔABC,
`"AC"/"BC" = cos45^circ`
`h/200 = 1/sqrt(2)`
`h = 200/sqrt(2) = (200sqrt(2))/2 = 100sqrt(2) = 100 xx 1.414 = 141.4`
Thus , the required distance is 141.4 m.
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