The angle of elevation of the top of a TV tow | vedclass

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

Question

(C) Let $OP = h$ be the height of the tower,where $O$ is the foot of the tower.In $	riangle OAP$,$\angle OAP = \alpha$. Thus,$OA = h \cot \alpha$.In

Vedclass · Accepted Answer

$a \sin 2 \alpha$

Vedclass · Answer

(C) Let $OP = h$ be the height of the tower,where $O$ is the foot of the tower.In $	riangle OAP$,$\angle OAP = \alpha$. Thus,$OA = h \cot \alpha$.In $	riangle OBP$,$\angle OBP = 2 \alpha$. Thus,$OB = h \cot 2 \alpha$.Given $AB = a$,we have $OA - OB = a$.Therefore,$h \cot \alpha - h \cot 2 \alpha = a$.$h (\frac{\cos \alpha}{\sin \alpha} - \frac{\cos 2 \alpha}{\sin 2 \alpha}) = a$.$h (\frac{\sin 2 \alpha \cos \alpha - \cos 2 \alpha \sin \alpha}{\sin \alpha \sin 2 \alpha}) = a$.Using the identity $\sin(A - B) = \sin A \cos B - \cos A \sin B$,we get:$h (\frac{\sin(2 \alpha - \alpha)}{\sin \alpha \sin 2 \alpha}) = a$.$h (\frac{\sin \alpha}{\sin \alpha \sin 2 \alpha}) = a$.$h (\frac{1}{\sin 2 \alpha}) = a$.$h = a \sin 2 \alpha$.Thus,the height of the tower is $a \sin 2 \alpha$.

The angle of elevation of the top of a $TV$ tower from three points $A, B, C$ in a straight line through the foot of the tower are $\alpha, 2 \alpha, 3 \alpha$ respectively. If $AB = a$,the height of the tower is

Similar Questions

From the top of a cliff,$60 \ m$ high,the angles of depression of the top and bottom of a tower are observed to be $30^{\circ}$ and $60^{\circ}$ respectively. Find the height of the tower in $m$.

$A$ tower stands on a horizontal plane. $A$ man on the ground $100 \ m$ from the base of the tower finds the angle of elevation of the top of the tower to be $30^{\circ}$. What is the height of the tower (in $m$)?

The angle of elevation of a tower from a distance $50 \; m$ from its foot is $30^{\circ}$. The height of the tower is

An observer on the top of a cliff,$200 \, m$ above the sea level,observes the angle of depression of two ships at anchor to be $45^{\circ}$ and $30^{\circ}$ respectively. Find the distance (in $m$) between the ships if the line joining them stretches to the base of the cliff.

$A$ person walking along a straight road towards a hill observes at two points,separated by a distance of $\sqrt{3} \text{ km}$,that the angles of elevation of the hill are $30^{\circ}$ and $60^{\circ}$. The height of the hill is

Vedclass Test Series

Exam Paper Generator

Online Exam Module