Two trees are standing on flat ground. The angle of elevation of the top of both the trees from a point $X$ on the ground is $40°$. If the horizontal distance between $X$ and the smaller tree is $8 \mathrm{m}$ and the distance of the top of the two trees is $20 \mathrm{m}$, calculate the horizontal distance between the two trees.

$\left(\cos 40°=0.7660\right)$

The horizontal distance between two buildings is $140 \mathrm{m}$. The angle of depression of the top of the first building when seen from the top of the second building is $30°$. If the height of the first building is $60 \mathrm{m}$, find the height of the second building

$(\sqrt{3}=1.732)$

From the top of a tower $50 \mathrm{m}$ high, the angles of depression of the top and bottom of a tree are observed to be $30°$ and $45°$ respectively. Find the height of the tree.

$(\sqrt{3}=1.732)$

As observed from the top of a $60 \mathrm{m}$ high lighthouse from the sea level, the angles of depression of two ships are $28°$ and $45°$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

$\left(\tan 28°=0.5317\right)$ 

man is watching a boat speeding away from the top of a tower. The boat makes an angle of depression of $60°$ with the man's eye when at a distance of $200 \mathrm{m}$ from the tower. After 10 seconds, the angle of depression becomes $45°$. What is the approximate speed of the boat (in $\mathrm{km}/\mathrm{hr}$), assuming that it is sailing in still water?

$(\sqrt{3}=1.732)$

From the top of a $12 \mathrm{m}$ high building, the angle of elevation of the top of a cable tower is $60°$ and the angle of depression of its foot is $30°$. Determine the height of the tower.

From a window ( $h$ metres high above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are ${\theta }_1$ and ${\theta }_2$ respectively. Show that the height of the opposite house is $h\left(1+\frac{\cot {\theta }_2}{\cot {\theta }_1}\right)$.