M L Aggarwal Solutions for Exercise 4: Chapter Test

An aeroplane $3000 \mathrm{m}$ high, passes vertically above another aeroplane at an instant when the angles of elevation of the two aeroplanes from the same point on the ground are ${60}^{°}$ and ${45}^{°}$ respectively. Find the vertical distance between the two planes (in $\mathrm{m}$).

A $7 \mathrm{m}$ long flagstaff is fixed on the top of a tower. From a point on the ground, the angles of elevation of the top and bottom of the flagstaff are $45°$ and $36°$ respectively. Find the height of the tower (in $\mathrm{m}$) correct to one place of decimal.

A boy, $1.6 \mathrm{m}$ tall, is $20 \mathrm{m}$ away from a tower and observes that the angle of elevation of the top of the tower is $60°$. Find the height of the tower (correct to $2$ decimal places).

A boy $1.54 \mathrm{m}$ tall can just see the sun over a wall $3.64 \mathrm{m}$ high which is $2.1 \mathrm{m}$ away from him. Find the angle of elevation of the sun (in $°$).

An aeroplane flying horizontally $1 \mathrm{km}$ above the ground is observed at an elevation of ${60}^{\mathrm{o}}$. After $10$ seconds, its elevation is observed to be $30°$. Find the speed of the aeroplane in $\mathrm{km}/\mathrm{h}$.

A man on the deck of a ship is $16 \mathrm{m}$ above the water level. He observes that the angle of elevation of the top of a cliff is $45°$ and the angle of depression of the base is $30°$. Calculate the distance of the cliff from the ship and the height of the cliff.

There is a small island in between a river $100 \mathrm{metres}$wide. A tall tree stands on the island. $P$ and$Q$ are points directly opposite to each other on the two banks and in the line with the tree. If the angles of elevation of the top of the tree from $P$ and $Q$ are $30°$ and $45°$ respectively, find the height of the tree (in decimal form correct for one decimal place). 

A man standing on the deck of the ship which is $20 \mathrm{m}$ above the sea-level, observes the angle of elevation of a bird as $30°$ and the angle of depression of its reflection in the sea as $60°$. Find the height of the bird.