Heights and Distances

An aeroplane when 900 m high passes vertically above another aeroplane at an instant when their angles of elevation at same observing point are 60° and 45° respectively. Approximately, how many meters higher is the one than the other?

A kite is flying at a height of $75\mathrm{m}$ above the ground. The inclination of the string with the ground is ${60}^0$ . Find the length of the string, assuming that there is no slack in the string.

At a point $P$ on the ground, the angle of elevation of the top of a $10\mathrm{m}$ tall building and of a helicopter hovering some distance over the top of the building are $30º$ and $60º$ respectively. Then, the height of the helicopter above the ground is

What is the angle of elevation of the sun when the length of the shadow of a vertical pole is equal to its height?

At a point $A$, the angle of elevation of a tower is found to be such that its tangent is $\frac{ 5}{12}$ . On walking $192 \mathrm{meter}$ towards the tower, the tangent of the angle of elevation is found to be $\frac{3}{4}$ . Find the height of the tower.the

The angles of depression of Two ships from the top of a lighthouse are $45°$ and $30°$ towards east, if the ships are $200 \mathrm{m}$ apart, the height of lighthouse is$?$ (Take $\sqrt{3}= 1.73$ )

If $D$ and $E$ are points on the sides $AB$ and $AC$ respectively of a $∆ABC$ such that $DE\parallel BC$. If $AD = x$, $DB = x - 2$, $AE = x + 2$ and $EC = x - 1$, then find the value of $x$.

Which is not correct?

A person stands at a height of $10 \mathrm{m}$ wants to get a fruit which is on a pole of height $\frac{50}{3} \mathrm{m}$ . If he stands at a distance of $\frac{20}{\sqrt{3} } \mathrm{m}$ from the foot of the pole horizontally, then the angle at which he should throw the stone, so that it hits the fruit is ______.

A telegraph post gets broken at a point against a storm and its top touches the ground at a distance $20 \mathrm{m}$ from the base of the post making an angle ${30}^{°}$ with the ground. What is the height of the post (in $\mathrm{m}$)?

A man is watching form the top of the tower a boat speeding away from the tower. The boat makes the angle of depression of $45°$ with the man's eye when at a distance of$60 \mathrm{m}$ from the tower. After $5 \sec$ the angle of depression becomes $30°$. What is the approximate speed of the boat, assuming that it is running in still water ?

The angle of elevation of the top of a tower from a point on the ground, which is$30\mathrm{m}$ away from the foot of the tower is $30$°. Find the height of the tower.

A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of ${45}^{°}$ with the man's eye when at a distance of $60 \mathrm{m}$ from the bottom of tower. After $5 \mathrm{seconds}$, the angle of depression becomes ${30}^{°}$. What is the approximate speed of the boat assuming that it is running in still water?

The sides of a triangle are $6\mathrm{cm}, 11\mathrm{cm}$ and $15\mathrm{cm}.$ The radius of its incircle is:

The top of a $15$$m$ high tower makes an angle of elevation of ${60}^0$ with the bottom of an electric pole and an angle of elevation of ${30}^0$ with the top of the pole. Find the height of the electric pole?

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height $h$. At a point on the plane, the angle of elevation of the bottom of the flag staff is $\alpha$ and that of the top of the flag staff is $\beta$. Find the height of the tower.

The angles of elevation of the top of a tower from the top and the foot of a pole of height $10\mathrm{m}$ are $30°$ and $60°$ respectively. Then the height of the tower is...-

$\mathrm{ABCD}$ is a square. The diagonals $\mathrm{AC} \mathrm{and} \mathrm{BD}$ meet at $\mathrm{O}$ . Let $\mathrm{K}, \mathrm{L}$ be the points on $\mathrm{AB}$ such that $\mathrm{AO} = \mathrm{AK}$, $\mathrm{BO}= \mathrm{BL}$. If $\angle \mathrm{LOK}=\mathrm{\theta }$, then what is the value of $\tan \mathrm{\theta }?$

Two boats leave a place at the same time. One travels $56 \mathrm{km}$ in the direction $\mathrm{N} 40° \mathrm{E}$, while the other travels $48 \mathrm{km}$ in the direction $\mathrm{S} 80° \mathrm{E}$. What is the distance between the boats?

The angle of depression of a vehicle on the ground from the top of a tower is $60°$. If the vehicle is at a distance of $100 \mathrm{meters}$ away from the building, find the height of the tower.