Karnataka Board Solutions for Chapter: Solved Examples, Exercise 9: Exercise 9

A tower stands vertically on the ground. From a point on the ground, which is $15 \mathrm{m}$ away from the foot of the tower, the angle of elevation of the top of the tower is found to be $60°$. Find the height of the tower.

An electrician has to repair an electric fault on a pole of height $5 \mathrm{m}$. She needs to reach a point $1.3 \mathrm{m}$ below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of $60°$ to the horizontal, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder? (You may take $\sqrt{3}=1.73$)

From a point $P$ on the ground, the angle of elevation of the top of a $10 \mathrm{m}$ tall building is $30°$. A flag is hoisted at the top of the building and the angle of elevation of the top of the flagstaff from $P$ is $45°$. Find the length of the flagstaff and the distance of the building from the point $P$. (Take $\sqrt{3}=1.732$).

The shadow of a tower standing on level ground is found to be $40 \mathrm{m}$ longer when the Sun’s altitude is $30°$ than when it is $60°$. Find the height of the tower.

The angles of depression of the top and the bottom of an $8 \mathrm{m}$ tall building from the top of a multi-storied building are $30°$ and $45°$, respectively. Find the height of the multi-storied building and the distance between the two buildings.

From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are $30°$ and $45°$, respectively. If the bridge is at a height of $3 \mathrm{m}$ from the banks, find the width of the river.