Heights and Distances

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 $\sqrt{3}= 1.73$ )

A man moves $\sqrt{2}x \mathrm{km}$ East from his residence and then moves $x \mathrm{km}$ North. He then goes $x \mathrm{km}$North-East and finally he takes a turn of $90°$ towards right and moves a distance $x \mathrm{km}$and reaches his office. What is the shortest distance of the office from his residence?

The angle of elevation of a boat from a $15 \mathrm{m}$ high bridge is $30°$. If boat is moving with the speed of $6 \mathrm{km}/\mathrm{hr},$ then time taken by the boat to get under the bridge is

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 $\mathrm{m}$)?

The horizontal distance between two towers is $60 m$. The angular elevation of the top of the taller tower as seen from the top of the shorter one is $30°$. If the height of the taller tower is $150 m$, the height of the shorter one approximately equal to_____.

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 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?

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...-

A fountain, $50 \mathrm{metres}$ off the base of a pillar on the same level ground was visible from $\frac{1^{rd}}{3}$ height of the pillar at $30º$angle of depression. Then the height of the pillar is

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.

A straight tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground making an angle of ${30}^{°}$ with the ground. The distance from the foot of the tree of the point where the top touches the ground is $10 \mathrm{m}$. The height of the tree (in $\mathrm{m}$) is ________.

Suppose the angle of elevation of the top of a tree at a point $\mathrm{E}$ due east of the tree is $60°$ and that at a point $\mathrm{F}$ due west of the tree is $30°$. If the distance between the points $\mathrm{E}$ and $\mathrm{F}$ is $160$ Feet, then what is the height of the tree?

The angle of depression of a point on the ground as seen from the top of a tower, $50 \mathrm{ft}$ high, is $45°$. Find the distance of the point on the ground from the foot of the tower.