A moving boat is observed from the top of a $150 \mathrm{m}$ high cliff moving away the cliff. The angle of depression of the boat changes from $60°$ to $45°$ in $2$ minutes. Find the speed of the boat in $\mathrm{m}/\mathrm{minute}$.

The shadow of a tower is found to be $40 m$ longer when the sun's altitude is $30°$ than when it was $60°$. Find the height of the tower. Given, $\sqrt{3}=1.732$

The sun of a tower standing on a level ground is found to be $20 m$ longer when the sun's altitude is $45°$ than when it is $60°$. Find the height of the tower. (Use $\sqrt{3}=1.73$).

Two ships are there on either side of a lighthouse in such a way that the ships and the lighthouse are in the same straight line. The angles of depression of two ships as observed from the top of the lighthouse are $60°$ and $45°$. If the height of the lighthouse is $200 m$, find the distance between the two ships. (Use $\sqrt{3}=1.73$)

On a straight line passing through the foot of tower, two points $C$ and $D$are at distances of $4 m$ and $16 m$ from the foot respectively. If the angles of elevation from $C$ and $D$ of the top of the tower are complementary, then find the height of the tower.

The angle of elevation of the top of a vertical tower from a point on the ground is $60°$. From another point $10 m$ vertically above the first point, its angle of elevation is $30°$. Find the height of the tower.

From the base of a $30 m$ high building, the angle of elevation of a tower is $60°$, and from the top of the building it is $30°$. Find the height of the tower and the distance between the building and the tower.

There are two poles, one each on either bank of a river just opposite to each other. One of the pole is $60 m$ high. From the top of this pole, the angles of depression of the top and foot of the other pole are $30°$ and $60°$ respectively. Find the width of the river and the height of the other pole.

The angle of elevation of the top $Q$ of a vertical tower $PQ$ from a point $X$ on the ground is $60°$. From a point $Y, 40 m$ vertically above $X$, the angle of elevation of the top $Q$ of the tower is $45°$.Find the height of the tower $PQ$ and the distance $PX$. (Use $\sqrt{3}=1.73$)