Question

Q.4.

A flagstaff of height 7 metres stands on the top of a tower. The angles subtended by the tower and the flagstaff to a point on the ground are 45° and 15° respectively. Find the height of the tower.with figure
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Answer 1

2.56m⠀

Step by Step Step-by-step explanation:

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Let AC be the 7 meters high Flagstaff

And BC be the tower

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Let the height of BC = x

The height of AB will be (x + 7)m

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∠ADB = 45° and ∠CDB = 15°

(as given in the question)

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By using trigonometry formula

`\sf \tan(A) = (perpendicular)/(base)`

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So tan 45 will be

`\sf \implies \tan45{ \degree} = (AB)/(BD) \\ \\ \sf \implies \tan45{ \degree} = (x + 7)/(BD) \\ \\ \sf \implies 1 = (x + 7)/(BD) \\ \\ \sf \implies BD = (x + 7)m`

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And tan 15 will be

`\sf \implies \tan15{ \degree} = (BC)/(BD) \\ \\ \sf \implies \tan15{ \degree} = (x)/(BD) \\ \\ \sf \implies 0.2679 = (x)/(BD) \\ \\ \sf \implies BD = (x)/(0.2679) \\ \\ \sf \implies BD = 3.7327x`

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Using both Values of BD to find x

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`\sf x + 7 = 3.7327x \\ \\ \sf 7 = 2.7327x \\ \\ \sf (7)/(2.7327) = x \\ \\ \sf \boxed{2.56 = x}`

The height of the tower is 2.56m