From an aeroplane vertically over a straight | vedclass

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

Question

(D) Let $h$ be the height of the aeroplane above the road.Let the two milestones be at points $A$ and $B$,and the point on the road directly below the

Vedclass · Accepted Answer

$\frac{	an \alpha \cdot 	an \beta}{	an \alpha + 	an \beta}$

Vedclass · Answer

(D) Let $h$ be the height of the aeroplane above the road.Let the two milestones be at points $A$ and $B$,and the point on the road directly below the aeroplane be $P$.Given that the distance between the two consecutive milestones is $1 	ext{ mile}$,so $AP + PB = 1$.In the right-angled triangles formed,we have $AP = h \cot \alpha$ and $PB = h \cot \beta$.Thus,$h \cot \alpha + h \cot \beta = 1$.$h(\cot \alpha + \cot \beta) = 1$.$h = \frac{1}{\cot \alpha + \cot \beta}$.Since $\cot 	heta = \frac{1}{	an 	heta}$,we have $h = \frac{1}{\frac{1}{	an \alpha} + \frac{1}{	an \beta}} = \frac{1}{\frac{	an \beta + 	an \alpha}{	an \alpha \cdot 	an \beta}} = \frac{	an \alpha \cdot 	an \beta}{	an \alpha + 	an \beta}$.

From an aeroplane vertically over a straight horizontal road,the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to be $\alpha$ and $\beta$. Then,the height in miles of the aeroplane above the road is:

Similar Questions

The angle of elevation of a stationary cloud from a point $2500 \ m$ above a lake is $15^{\circ}$ and from the same point the angle of depression of its reflection in the lake is $45^{\circ}$. The height (in metres) of the cloud above the lake, given that $\cot 15^{\circ}=2+\sqrt{3}$, is

The upper part of a tree broken by the wind makes an angle of $30^\circ$ with the ground. The distance from the root to the point where the top of the tree touches the ground is $10 \, m$. What was the original height of the tree in meters?

$A$ $20 \ m$ high flag pole is fixed on an $80 \ m$ high pillar. At a point on the ground $50 \ m$ away from the base of the pillar,the flag pole subtends an angle $\alpha$. Find the value of $\tan \alpha$.

If the angle of depression of a point $A$ on the ground from the top of a tower is $30^\circ$,then the angle of elevation of the top of the tower from the point $A$ will be .............. $^\circ $.

Vedclass Test Series

Exam Paper Generator

Online Exam Module