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

The length of the shadow of a tower is $9 \text{ m}$ when the sun's altitude is $30^{\circ}$. What is the height of the tower? (In $m$)

The angle of elevation of the top of a tower from a point $20 \ m$ away from its base is $45^{\circ}$. The height of the tower is (in $m$):

The ratio of the length of a rod and its shadow is $1 : \sqrt{3}$. The angle of elevation of the sun is (in $^{\circ}$)

$A$ 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

At a point,$15 \, m$ away from the base of a $15 \, m$ high house,the angle of elevation of the top is (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module