Two poles are x metres apart and the height o | vedclass

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

Question

(D) Let the height of the shorter pole be $h$ and the height of the taller pole be $2h$.Let the distance between the two poles be $x$.The midpoint of

Vedclass · Accepted Answer

$\frac{x}{2 \sqrt{2}}$

Vedclass · Answer

(D) Let the height of the shorter pole be $h$ and the height of the taller pole be $2h$.Let the distance between the two poles be $x$.The midpoint of the line joining their feet divides the distance $x$ into two equal parts,each of length $\frac{x}{2}$.Let the angles of elevation from the midpoint be $	heta$ and $90^\circ - 	heta$.For the shorter pole: $	an(90^\circ - 	heta) = \frac{h}{x/2} = \frac{2h}{x}$.Since $	an(90^\circ - 	heta) = \cot 	heta$,we have $\cot 	heta = \frac{2h}{x}$.For the taller pole: $	an 	heta = \frac{2h}{x/2} = \frac{4h}{x}$.Multiplying the two equations: $	an 	heta \cdot \cot 	heta = \left(\frac{4h}{x}ight) \cdot \left(\frac{2h}{x}ight)$.$1 = \frac{8h^2}{x^2}$.$h^2 = \frac{x^2}{8}$.$h = \sqrt{\frac{x^2}{8}} = \frac{x}{2\sqrt{2}}$.

Two poles are $x$ metres apart and the height of one is double than that of the other. If from the midpoint of the line joining their feet,an observer finds the angle of elevation of their tops to be complementary,then the height of the shorter pole is $\ldots \ldots \ldots \ldots$

Similar Questions

$A$ pole stands on the ground. Watching from the top of the pole,the angle of depression of a stone on the ground $10 \, m$ away from the pole is $60^{\circ}$. Then the height of the pole is $\ldots \ldots \ldots \, m$. (Take $\sqrt{3} = 1.73$.)

Watching from the top of a tower,the angles of depression of two houses $A$ and $B$ are found to be $25^{\circ}$ and $40^{\circ}$ respectively. Then,.......

In a right triangle,if the measure of one of the angles is $45^{\circ}$,then the measure of the side opposite to the angle with measure $45^{\circ}$ is $\ldots \ldots \ldots$ times the measure of the hypotenuse.

Vedclass Test Series

Exam Paper Generator

Online Exam Module