From the top A of a vertical wall AB of heigh | vedclass

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

Question

(A) Let $AB = 30 \ m$. Let $BQ = x$. In $	riangle ABQ$,$	an 60^{\circ} = \frac{AB}{BQ} = \frac{30}{x}$.So,$x = \frac{30}{\sqrt{3}} = 10\sqrt{3} \ m$

Vedclass · Accepted Answer

$600(\sqrt{3}-1)$

Vedclass · Answer

(A) Let $AB = 30 \ m$. Let $BQ = x$. In $	riangle ABQ$,$	an 60^{\circ} = \frac{AB}{BQ} = \frac{30}{x}$.So,$x = \frac{30}{\sqrt{3}} = 10\sqrt{3} \ m$. Thus,$BQ = 10\sqrt{3} \ m$.Since $BCPQ$ is a rectangle,$CP = BQ = 10\sqrt{3} \ m$ and $PQ = BC$.In $	riangle ACP$,the angle of depression of $P$ is $15^{\circ}$,so $\angle ACP = 90^{\circ}$ and $\angle CAP = 90^{\circ} - 15^{\circ} = 75^{\circ}$ is not correct,rather $\angle APC = 15^{\circ}$ (alternate interior angle).Thus,$	an 15^{\circ} = \frac{AC}{CP} = \frac{AC}{10\sqrt{3}}$.Since $	an 15^{\circ} = 2 - \sqrt{3}$,we have $AC = 10\sqrt{3}(2 - \sqrt{3}) = 20\sqrt{3} - 30$.Then $BC = AB - AC = 30 - (20\sqrt{3} - 30) = 60 - 20\sqrt{3}$.Area of rectangle $BCPQ = BQ 	imes BC = (10\sqrt{3})(60 - 20\sqrt{3}) = 600\sqrt{3} - 200(3) = 600\sqrt{3} - 600 = 600(\sqrt{3} - 1) \ m^2$.

Similar Questions

The angle of elevation of a stationary cloud from a point $2500 \, m$ above a lake is $15^\circ$ and the angle of depression of its reflection in the lake is $45^\circ$. The height of the cloud above the lake level is

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

An aeroplane flying with uniform speed horizontally $1 \ km$ above the ground is observed at an elevation of $60^{\circ}$. After $10 \ s$, if the elevation is observed to be $30^{\circ}$, then the speed of the plane (in $km/h$) is

$A$ 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.

Vedclass Test Series

Exam Paper Generator

Online Exam Module