Question

A tower of height b subtends an angle at a point O on the level of the foot of the tower and at a distance a from the foot of the tower. If a pole mounted on the tower also subtends an equal angle at O, the height of the pole is.

• A. $b \left( \frac { a ^ { 2 } - b ^ { 2 } } { a ^ { 2 } + b ^ { 2 } } \right)$
• B. $b \left( \frac { a ^ { 2 } + b ^ { 2 } } { a ^ { 2 } - b ^ { 2 } } \right)$
• C. $a \left( \frac { a ^ { 2 } - b ^ { 2 } } { a ^ { 2 } + b ^ { 2 } } \right)$
• D. $a \left( \frac { a ^ { 2 } + b ^ { 2 } } { a ^ { 2 } - b ^ { 2 } } \right)$

Answer 1

Answer: (B)

$b \left( \frac { a ^ { 2 } + b ^ { 2 } } { a ^ { 2 } - b ^ { 2 } } \right)$

Answer 2

Let AB is tower and AC is pole of height h.

From $\triangle A B O , \frac { b } { a } = \tan \alpha$ ......(i)

From $\frac { b + h } { a } = \frac { 2 \tan \alpha } { 1 - \tan ^ { 2 } \alpha }$

or $b + h = \frac { 2 a \frac { b } { a } } { 1 - \frac { b ^ { 2 } } { a ^ { 2 } } }$ (Put value of $\tan \alpha$ from (i))

or $h = \frac { b \left( a ^ { 2 } + b ^ { 2 } \right) } { a ^ { 2 } - b ^ { 2 } }$.

Remember the result $h = \frac { b \left( a ^ { 2 } + b ^ { 2 } \right) } { a ^ { 2 } - b ^ { 2 } }$ in which $b =$ height of tower, $h =$ height of pole, a = distance of observation point from the tower