Two lizards \(A\) and \(B\), are on the ground. They spotted a spider(prey) on the wall at a distance of 36 \(cm\) from the ground and at an angle of elevation 30\(^{\circ}\) and 60\(^{\circ}\), respectively. They both start simultaneously and with the same speed along the shortest path to catch their prey. Find which lizard will catch its prey first?
Answer:
Let \(A\) and \(B\) denote the position of two lizards on the ground.
Let \(C\) be the position of the spider(prey) on the wall.
Draw \(CD \perp AB\). Let \(CD\) denote the distance of the spider from the ground.
\(AC=\)
\(CB=\)
The lizard that first catches its prey is