A 20 m high flag pole is fixed on an 80 m h | vedclass

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(B) Let the base of the pillar be $B$ and the point on the ground be $A$. The top of the pillar is $C$ and the top of the flag pole is $D$. Given $AB

Vedclass · Accepted Answer

$\frac{2}{21}$

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(B) Let the base of the pillar be $B$ and the point on the ground be $A$. The top of the pillar is $C$ and the top of the flag pole is $D$. Given $AB = 50 \ m$,$BC = 80 \ m$,and $CD = 20 \ m$.Let $\angle CAB = \beta$. In $	riangle ABC$,$	an \beta = \frac{BC}{AB} = \frac{80}{50} = \frac{8}{5}$.In $	riangle ABD$,the total height $BD = BC + CD = 80 + 20 = 100 \ m$.Then $	an(\alpha + \beta) = \frac{BD}{AB} = \frac{100}{50} = 2$.Using the formula $	an(\alpha + \beta) = \frac{	an \alpha + 	an \beta}{1 - 	an \alpha 	an \beta}$,we have:$\frac{	an \alpha + \frac{8}{5}}{1 - 	an \alpha \cdot \frac{8}{5}} = 2$$	an \alpha + \frac{8}{5} = 2 - \frac{16}{5} 	an \alpha$$	an \alpha + \frac{16}{5} 	an \alpha = 2 - \frac{8}{5}$$\frac{21}{5} 	an \alpha = \frac{2}{5}$$	an \alpha = \frac{2}{21}$.

$A$ $20 \ m$ high flag pole is fixed on an $80 \ m$ high pillar. At a point on the ground $50 \ m$ away from the base of the pillar,the flag pole subtends an angle $\alpha$. Find the value of $\tan \alpha$.

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