Q1. Let height be $h, canal width $x. $\tan 60^\circ = h/x \rightarrow h = x\sqrt{3}. $\tan 30^\circ = h/(x+20) \rightarrow \sqrt{3} = (x+20)/x\sqrt{3} \rightarrow 3x = x+20 \rightarrow x=10\text{ m}, h=10\sqrt{3}\text{ m}$.
Q2. Height of multi-storeyed building is $4(3+\sqrt{3})\text{ m}, and distance between buildings is $4(3+\sqrt{3})\text{ m}$.
Q3. Let distance between ships be $x. $75 = (d) \tan 45^\circ \rightarrow d = 75\text{ m}. For other ship, $(75+x)\tan 30^\circ = 75 \rightarrow x = 75(\sqrt{3}-1)\text{ m}$.
Q4. Height of balloon above girl's eyes is $88.2 - 1.2 = 87\text{ m}. Distance traveled $d = 87\sqrt{3} - 87/\sqrt{3} = 58\sqrt{3}\text{ m}$.
Q5. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are $45^\circ$ and $60^\circ$ respectively. Find the height of the tower.
