Two points $A$ and $B$ are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are $60°$ and $45°$ respectively. The height of the tower is $15 \mathrm{m},$ and if the distance between these points is $k \mathrm{m}$ (Correct up to two decimal places) then find $k$. [Take $\sqrt{3}=1.732$]

A man on the deck of a ship is $10 \mathrm{m}$ 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 $30°$. If height of the cliff is $k \mathrm{m}$, then write the value of $k$ as final answer. [Take $\sqrt{3}=1.732$]

A man standing on the deck of a ship, which is $8 \mathrm{m}$ above water level. He observes the angle of elevation of the top of a hill as $60°$ and the angle of depression of the base of the hill as $30°$. If the height of the hill is $k \mathrm{m}$, then write the value of $k$ as final answer.

There are two temples, one on each bank of a river, just opposite to each other. One temple is $50 \mathrm{m}$ high. From the top of this temple, the angles of depression of the top and the foot of the other temple are $30°$ and $60°$ respectively. If the height of the other temple (correct to two decimal places) is $k \mathrm{m}$, then write the value of $k$ as final answer. [$\mathrm{Take} \sqrt{3}=1.732$]

The angle of elevation of an aeroplane from a point on the ground is $45°$. After a flight of $15$ seconds, the elevation changes to $30°$. The aeroplane is flying at a height of $3000$ metres. If the speed of the aeroplane is of the form $y \mathrm{km}/\mathrm{h}$, then find the value of $y$. [Take $\sqrt{3}=1.732$]