Question

The angle of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances $49m$ and $36m$ are ${43}^{\circ }$ and ${47}^{\circ }$ respectively. What is the height of the tower?

• A. $40m$
• B. $42m$
• C. $45m$
• D. $47m$

Answer 1

The correct option is B $42m$

Let $BD$ be the tower

In triangle $ABD$

$\tan A=\frac{BD}{AB}⟹\tan {43}^o=\frac{BD}{49}⟹BD=49\tan {43}^o$

In triangle $BDC$

$\tan C=\frac{BD}{BC}⟹\tan {47}^o=\frac{BD}{36}⟹BD=36\tan {47}^o$

$⟹36\tan {47}^o=49\tan {43}^o⟹\frac{\tan {47}^o}{\tan {43}^o}=\frac{49}{36}⟹\frac{\tan {47}^o}{\cot {47}^o}=\frac{49}{36}⟹{\tan }^2{47}^o=\frac{49}{36}⟹\tan {47}^o=\frac{7}{6}$

But $BD=36\tan {47}^o$

$⟹BD=36\times \frac{7}{6}=42m$