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

If a flagstaff of $6 \, m$ height placed on the top of a tower throws a shadow of $2 \sqrt{3} \, m$ along the ground,then the angle that the sun makes with the ground is

From the top of a $60 \ m$ high lighthouse with its base at sea level,the angle of depression of a boat is $15^{\circ}$. The distance of the boat from the lighthouse is

Two towers of equal height stand on either side of a wide road which is $100 \, m$ wide. At a point on the road between the towers, the angles of elevation of the tops of the towers are $60^{\circ}$ and $30^{\circ}$. Find their heights in metres. (in $\sqrt{3}$)

$A$ $10 \ m$ long ladder is placed against a wall. It is inclined at an angle of $30^{\circ}$ to the ground. The distance (in $m$) of the foot of the ladder from the wall is (Given $\sqrt{3} = 1.732$)

Two posts are $x \text{ m}$ apart and the height of one is double that of the other. If from the midpoint of the line joining their feet,an observer finds the angular elevations of their tops to be complementary,then the height (in $\text{m}$) of the shorter post is

Vedclass Test Series

Exam Paper Generator

Online Exam Module