An electrician has to repair an electric fault on a pole of height $4$ metres. He needs to reach a point $1$ metre below the top of the pole to undertake the repair work. What should be the length of the ladder that he should use, which when inclined at an angle of $60°$ to the horizontal would enable him to reach the required position? [Use $\sqrt{3}=1.73$]

From the top of a building $\mathrm{AB}, 60 \mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp post $\mathrm{CD}$ are observed to be $30°$ and $60°$, respectively. If the horizontal distance between $\mathrm{AB}$ and $\mathrm{CD}$ is $x \mathrm{m}$, then find the value of $x$ correct to one decimal place. [Take $\sqrt{3}=1.732$]

From the top of a building $\mathrm{AB}, 60 \mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp post $\mathrm{CD}$ are observed to be $30°$ and $60°$, respectively. Find the height of the lamp post,

From the top of a building $\mathrm{AB}, 60 \mathrm{m}$ high, the angles of depression of the top and bottom of a vertical lamp post $\mathrm{CD}$ are observed to be $30°$ and $60°$, respectively. Find the difference between the heights of the building and the lamp post.