Answer
2.56m⠀
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
[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]
The height of the tower is 2.56m
