H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Heights & Distances, Exercise 2: REVISION EXERCISE

A man standing on the deck of a ship which is $10 \mathrm{m}$ above the sea level, observes the angle of elevation of the top of the cloud as $30°$ and angle of depression of its reflection in the sea was found to be $60°.$ Find the height of the cloud and also the distance of the cloud from the man.

The angle of elevation of a cloud from a point $60 \mathrm{m}$ above the lake is $30°$ and the angle of depression of its reflection in the lake is $60°$. Find the height of the cloud above the lake in $\mathrm{m}$.

The shadow of a vertical tower on level ground increases by $16 \mathrm{m}$ when the altitude of the sun changes from angles of elevation $60°$ to $45°$. If the height of the tower is $k \mathrm{m}$, find the value of $k$ corrected to two decimal places considering $\sqrt{3}=1.73$.

From a window, $60 \mathrm{m}$ high above the ground, of a house in a street, the angles of elevation and depression of the top and foot of another house on the opposite side of the street are $60°$ and $45°$ respectively. Show that the height of the opposite house is $60(1+\sqrt{3})$ metres.

Two pillars of equal heights are on either side of a road, which is $100 \mathrm{m}$ wide. The angles of elevation of the top of the pillars are $60°$ and $30°$ at a point on the road between the pillars. Find the position of the point between the pillars on the road and the height of the pillars.

From the top of a building $60 \mathrm{m}$ high the angles of depression of the top and the bottom of a tower are observed to be $30°$ and $60°$ respectively. Find the height of the tower in $\mathrm{m}$.

The height of a mountain is $k\sqrt{3} \mathrm{km}$ if the elevation of its top at an unknown distance from the base is $60°$ and at a distance $10 \mathrm{km}$ further off from the mountain, along the same line, the angle of elevation is $30°$, then find the value of $k$.

Two men on either side of a cliff, $60 \mathrm{m}$ high, observe the angles of elevation of the top of the cliff to be $45°$ and $60°$ respectively. The distance between two men is $k\left(3+\sqrt{3}\right) \mathrm{m}$. Find $k$.