R K Bansal Solutions for Exercise 1: EXERCISE

From the top of a cliff, $60$ metres high, the angles of depression of the top and bottom of a tower are observed to be $30°$ and $60°$. Find the height of the tower.

A man on a cliff observes a boat, at an angle of depression $30°$, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be $60°$. Assuming that the boat sails at a uniform speed, determine how much more time it will take to reach the shore ?

A man on a cliff observes a boat, at an angle of depression $30°$, which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be $60°$. Assuming that the boat sails at a uniform speed, determine the speed of the boat in metre per second, if the height of the cliff is $500\mathrm{m}$.

A man in a boat rowing away from a lighthouse $150 \mathrm{m}$ high, takes $2$ minutes to change the angle of elevation of the top of the lighthouse from $60°$ to $45°$. Find the speed of the boat.

The horizontal distance between two towers is $75 \mathrm{m}$ and the angular depression of the top of the first tower as seen from the top of the second, which is $160 \mathrm{m}$ high, is $45°$. Find the height of the first tower.

The length of the shadow of a tower standing on level plane is found to be $2\mathrm{y}$ meters longer when the sun's altitude is $30°$ than when it was $45°$. If the height of the tower is $\mathrm{ky}(\sqrt{m}+n)$ meters, then $k+m+n=$

An aeroplane flying horizontally $1\mathrm{km}$ above the ground and going away from the observer is observed at an elevation of $60°$. After $10$ seconds, its elevation is observed to be $30°$; find the uniform speed of the aeroplane in $\mathrm{km}$ per hour.

From the top of a hill, the angles of depression of two consecutive kilometre stones, due east, are found to be $30°$ and $45°$ respectively. Find the distances of the two stones from the foot of the hill.