At a distance 2h from the foot of a tower of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the height of the pole be $p$. The tower has height $h$ and is at a distance $2h$ from the observer.Let the angle subtended by the tower be $\

Vedclass · Accepted Answer

$\frac{5h}{3}$

Vedclass · Answer

(A) Let the height of the pole be $p$. The tower has height $h$ and is at a distance $2h$ from the observer.Let the angle subtended by the tower be $\alpha$. Then,$	an \alpha = \frac{h}{2h} = \frac{1}{2}$.Let the pole be on top of the tower. The angle subtended by the pole is also $\alpha$.The total angle subtended by the tower and the pole together is $\alpha + \alpha = 2\alpha$.The total height is $h + p$.Thus,$	an(2\alpha) = \frac{h + p}{2h}$.Using the formula $	an(2\alpha) = \frac{2	an \alpha}{1 - 	an^2 \alpha}$,we get:$\frac{h + p}{2h} = \frac{2(1/2)}{1 - (1/2)^2} = \frac{1}{1 - 1/4} = \frac{1}{3/4} = \frac{4}{3}$.Therefore,$\frac{h + p}{2h} = \frac{4}{3}$ $\Rightarrow h + p = \frac{8h}{3}$ $\Rightarrow p = \frac{8h}{3} - h = \frac{5h}{3}$.

At a distance $2h$ from the foot of a tower of height $h$,the tower and a pole at the top of the tower subtend equal angles. The height of the pole is:

Similar Questions

The angles of elevation of the top of a tower $A$ from the top $B$ and bottom $D$ of a building of height $a$ are $30^\circ$ and $45^\circ$ respectively. If the tower and the building stand at the same level,then the height of the tower is

$A$ person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^\circ$. When he moves $40 \ m$ away from the bank,he finds the angle to be $30^\circ$. The breadth of the river is.....$m$

If a flag-staff of $6 \ m$ high placed on the top of a tower throws a shadow of $2 \sqrt{3} \ m$ along the ground,then the angle (in degrees) that the sun makes with the ground is.....$^o$

$A$ person standing at a distance of $10 \ m$ from a pole observes that the angle subtended by the lower $\frac{1}{3}$rd part and the upper $\frac{2}{3}$rd part of the pole are the same. Find the height of the pole.

The base of a cliff is circular. From the extremities of a diameter of the base,the angles of elevation of the top of the cliff are $30^\circ$ and $60^\circ$. If the height of the cliff is $500 \ m$,then the diameter of the base of the cliff is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module