Jitender Gupta and Divya Malik Solutions for Exercise 2: ARCHIVES (Last 8 Years)

The angle of depression of two ships $A$ and $\mathrm{B}$ as observed from the top of a light-house $60 \mathrm{m}$ high are $60°$ and $45°$, respectively. If the two ships are on the opposite sides of the light-house, then find the distance between the two ships. Give your answer correct to the nearest whole number.

An aeroplane at an altitude of $1500 \mathrm{m}$ finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are $45°$ and $30°$, respectively. Find the distance between the two ships in metres.

The horizontal distance between two towers is $120 \mathrm{m}$. The angle of elevation of the top and angle of depression of the bottom of the first tower as observed from the second tower are $30°$ and $24°$, respectively. Find the heights of the two towers.

An aeroplane at an altitude of $250 \mathrm{m}$ observes the angles of depression of two boats on the opposite banks of a river to be $45°$ and $60°$, respectively. Find the width of the river. Write the answer correct to the nearest whole number in metres.

In the adjoining figure, from the top of a building $AB=60 \mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp-post $CD$ are observed to be $30°$ and $60°$, respectively. Find the horizontal distance observed (in metres) between $AB$ and $CD$.

In the adjoining figure, from the top of a building $AB$$=60 \mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp-post $CD$ are observed to be $30°$ and $60°$, respectively. Find the height of the lamp-post in metres.

As observed from the top of a $80 \mathrm{m}$ tall lighthouse, the angles of depression of two ships on the same side of the lighthouse in a horizontal line with its base are $30°$and $40°$, respectively. Find the distance between the two ships. Give your answer correct to the nearest metres.

A man observes the angle of elevation of the top of a building to be $30°$ He walks towards it in a horizontal line through its base. On covering $60 \mathrm{m}$, the angle of elevation changes to $60°$. Find the height of the building correct to the nearest meters.