Question : The elevation angles of the top and bottom of a flag kept on a flagpost from a 30 metres distance are 45° and 30°, respectively. Height of the flag is: $\left (\text {taking} \;\sqrt{3}= 1.732 \right )$
Option 1: $12\sqrt{3}$ metres
Option 2: 15 metres
Option 3: 14.32 metres
Option 4: 12.68 metres
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Correct Answer: 12.68 metres
Solution :
In $\triangle ABC$
$\tan 30°=\frac{BC}{AB}$
⇒ $\frac{1}{\sqrt{3}}=\frac{BC}{30}$
⇒ $BC=\frac{30}{\sqrt{3}}$ m
In $\triangle ABD$
$\tan 45°=\frac{BC+DC}{AB}$
⇒ $1=\frac{\frac{30}{\sqrt{3}}+h}{30}$
⇒ $\frac{30}{\sqrt{3}}+h=30$
⇒ $h=30–\frac{30}{\sqrt{3}}=30[1–\frac{1}{\sqrt{3}}]$
⇒ $h=\frac{30}{3}\times(3–\sqrt{3})$
⇒ $h=10\times(3–1.732)=12.68$ m
Hence, the correct answer is 12.68 m.
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