The angles of elevation of the top of a tower | vedclass

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

Question

(A) Let $AB$ be the tower of height $h$ units.Let the points $P$ and $Q$ be at distances $PB = a$ and $QB = b$ from the base $B$ of the tower.Given th

Vedclass · Accepted Answer

$\sqrt{ab}$

Vedclass · Answer

(A) Let $AB$ be the tower of height $h$ units.Let the points $P$ and $Q$ be at distances $PB = a$ and $QB = b$ from the base $B$ of the tower.Given that the angles of elevation are complementary,let $\angle AQB = 	heta$ and $\angle APB = 90^{\circ} - 	heta$.In $	riangle AQB$,$	an 	heta = \frac{AB}{QB} = \frac{h}{b}$.In $	riangle APB$,$	an(90^{\circ} - 	heta) = \frac{AB}{PB} = \frac{h}{a}$.Since $	an(90^{\circ} - 	heta) = \cot 	heta$,we have $\cot 	heta = \frac{h}{a}$.Multiplying the two equations: $	an 	heta \cdot \cot 	heta = \left(\frac{h}{b}ight) \cdot \left(\frac{h}{a}ight)$.Since $	an 	heta \cdot \cot 	heta = 1$,we get $1 = \frac{h^2}{ab}$.Therefore,$h^2 = ab$,which implies $h = \sqrt{ab}$.

The angles of elevation of the top of a tower from the points $P$ and $Q,$ at distances of $a$ and $b$ respectively from the base of the tower and in the same straight line with it,are complementary. The height of the tower is

Similar Questions

The angle of elevation of the top of an unfinished tower at a point distant $120 \ m$ from its base is $45^{\circ}$. If the elevation of the top at the same point is to be $60^{\circ}$,the tower must be raised to a height of:

The tops of two poles of height $20 \ m$ and $14 \ m$ are connected by a wire. If the wire makes an angle $30^{\circ}$ with the horizontal,then the length of the wire is $m$.

Two posts are $x \text{ m}$ apart and the height of one is double that of the other. If from the midpoint of the line joining their feet,an observer finds the angular elevations of their tops to be complementary,then the height (in $\text{m}$) of the shorter post is

From the top of a $25 \ m$ high cliff,the angle of elevation of a tower is found to be equal to the angle of depression of the foot of the tower. Find the height of the tower in $m$.

From a point $20 \; m$ away from the foot of a tower,the angle of elevation of the top of the tower is $30^{\circ}$. The height of the tower is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module