Answer

2.56m⠀

StepbyStepexplanation:

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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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Byusingtrigonometryformula

[tex] \sf \tan(A) = \frac{perpendicular}{base} [/tex]

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So tan 45 will be

[tex] \sf \implies \tan45{ \degree} = \frac{AB}{BD} \\ \\ \sf \implies \tan45{ \degree} = \frac{x + 7}{BD} \\ \\ \sf \implies 1 = \frac{x + 7}{BD} \\ \\ \sf \implies BD = (x + 7)m[/tex]

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And tan 15 will be

[tex] \sf \implies \tan15{ \degree} = \frac{BC}{BD} \\ \\ \sf \implies \tan15{ \degree} = \frac{x}{BD} \\ \\ \sf \implies 0.2679 = \frac{x}{BD} \\ \\ \sf \implies BD = \frac{x}{0.2679} \\ \\ \sf \implies BD = 3.7327x[/tex]

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Using both Values of BD to find x

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[tex] \sf x + 7 = 3.7327x \\ \\ \sf 7 = 2.7327x \\ \\ \sf \frac{7}{2.7327} = x \\ \\ \sf \boxed{2.56 = x}[/tex]

Theheightofthetoweris2.56m