A vertical pole subtends an angle tan ^{-1}le | vedclass

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

Question

(C) Let the pole be $AC$ of height $2h$, where $B$ is the midpoint such that $AB = BC = h$. Let $PA = x$. The angle subtended by the whole pole is $

Vedclass · Accepted Answer

$\left(\frac{2}{9}, \frac{1}{4}\right)$

Vedclass · Answer

(C) Let the pole be $AC$ of height $2h$, where $B$ is the midpoint such that $AB = BC = h$. Let $PA = x$. The angle subtended by the whole pole is $	heta = 	an^{-1}\left(\frac{1}{2}ight)$, so $	an 	heta = \frac{2h}{x} = \frac{1}{2}$, which implies $x = 4h$.Now, $	an(	heta + \beta) = \frac{2h}{x} = \frac{1}{2}$ and $	an \beta = \frac{h}{x} = \frac{h}{4h} = \frac{1}{4}$.Since $	heta = \alpha + \beta$, we have $\alpha = 	heta - \beta$.Using the formula $	an \alpha = 	an(	heta - \beta) = \frac{	an 	heta - 	an \beta}{1 + 	an 	heta 	an \beta} = \frac{\frac{1}{2} - \frac{1}{4}}{1 + (\frac{1}{2})(\frac{1}{4})} = \frac{\frac{1}{4}}{1 + \frac{1}{8}} = \frac{\frac{1}{4}}{\frac{9}{8}} = \frac{1}{4} 	imes \frac{8}{9} = \frac{2}{9}$.Thus, $(	an \alpha, 	an \beta) = \left(\frac{2}{9}, \frac{1}{4}ight)$.

$A$ vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles subtended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and $\beta$, then $(\tan \alpha, \tan \beta)$ is equal to

Similar Questions

$A$ tower, of $x$ metres high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant $y$ metres from the foot of the tower. Then, the length of the flagstaff (in metres) is:

$A$ man from the top of a $100 \ m$ high tower sees a car moving towards the tower at an angle of depression of $30^\circ$. After some time,the angle of depression becomes $60^\circ$. The distance (in meters) travelled by the car during the time is

$A$ house of height $100 \ m$ subtends a right angle at the window of an opposite house. If the height of the window is $64 \ m$,then the distance between the two houses is......$m$.

$A$ man whose eye level is $1.5 \ m$ above the ground observes the angle of elevation of a tower to be $60^\circ$. If the distance of the man from the tower is $10 \ m$,the height of the tower is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module