From an aeroplane vertically over a straight | vedclass

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

Question

(A) Let $H$ be the height of the aeroplane above the road in miles.Let $P$ be the position of the aeroplane and $Q$ be the point on the road directly

Vedclass · Accepted Answer

$\frac{\sqrt{3}}{2}$

Vedclass · Answer

(A) Let $H$ be the height of the aeroplane above the road in miles.Let $P$ be the position of the aeroplane and $Q$ be the point on the road directly below it.Let $R$ and $S$ be the positions of the two consecutive milestones on the road.The distance between two consecutive milestones is $RS = 1 	ext{ mile}$.In $\Delta PQR$,$	an 60^{\circ} = \frac{H}{QR} \Rightarrow QR = \frac{H}{\sqrt{3}}$.In $\Delta PQS$,$	an 30^{\circ} = \frac{H}{QS} \Rightarrow QS = H\sqrt{3}$.Since $QS = QR + RS$,we have $H\sqrt{3} = \frac{H}{\sqrt{3}} + 1$.Multiplying by $\sqrt{3}$,we get $3H = H + \sqrt{3}$.$2H = \sqrt{3} \Rightarrow H = \frac{\sqrt{3}}{2} 	ext{ miles}$.

From an aeroplane vertically over a straight horizontal road,the angles of depression of two consecutive milestones on the opposite sides of the aeroplane are observed to be $30^{\circ}$ and $60^{\circ}$. Find the height in miles of the aeroplane above the road.

Similar Questions

On the level ground,the angle of elevation of the top of the tower is $30^{\circ}$. On moving $20 \ m$ nearer,the angle of elevation is $60^{\circ}$. The height of the tower is (in $m$):

$A$ $20 \, m$ high electric pole stands upright on the ground with the help of a steel wire attached to its top and fixed on the ground. If the steel wire makes an angle of $60^{\circ}$ with the horizontal ground,find the length of the steel wire (in $m$).

$A$ tower subtends an angle of $30^{\circ}$ at a point on the same level as the foot of the tower. At a second point,$h \ m$ above the first,the angle of depression of the foot of the tower is $60^{\circ}$. The horizontal distance of the tower from the point is

From the top of a tower of height $108 \; m$,the angles of depression of two objects on either side of the tower are $30^{\circ}$ and $45^{\circ}$. The distance between the objects is:

When the length of the shadow of a pole is equal to the height of the pole,then the angle of elevation of the source of light is: (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module