Two ships are there in the sea on either of a lighthouse in such away that the ships and the lighthouse are in the same straight line. The angle of depression of two ships are observed from the top of the lighthouse are $60°$ and $45°$ respectively. If the height of the lighthouse is $200 \mathrm{m}$ and the distance between the two ships is $k \mathrm{m}$, then find the value of $k$ (correct up to two decimal places). $(\sqrt{3}=1.732)$

The horizontal distance between the two poles is $15 \mathrm{m}$. The angle of depression of the top of the first pole as seen from the top of the second pole is $30°$. If the height of the second pole is $24 \mathrm{m}$, find the height of the first pole in metres. $(\sqrt{3}=1.732)$(Write only the numeral values without units correct upto 2 decimal places)

The angle of depression of two ships from the top of a light house and on the same side of it are found to be $45°$ and $30°$ respectively. If the ships are $200 \mathrm{m}$ apart, find the height of the light house in metres. (Write only the numeral values without units)[Take $\sqrt{3}=1.732$]

The angles of elevation of the top of a tower from two points at a distance of $4 \mathrm{m}$ and $9 \mathrm{m}$ from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is $6 \mathrm{m}.$

The horizontal distance between two trees of different heights is $60 \mathrm{m}$. The angle of depression of the top of the first tree when seen from the top of the second tree is $45°$. The height of the second tree is $80 \mathrm{m}$. If the height of the first tree is $h \mathrm{m}$, then find the value of $h$.