Question

A dog chases a kitten who starts climbing up a tree to protect itself from the dog. After climbing a height of 24 feet, it finds itself stuck and unable to climb down out of fear. Fire fighters are pressed into service to get the kitten down. But they have a problem. There ladder is 25 feet and they can go as close as 10 feet from the foot of the tree. Do you think at this distance, they will be able to rescue the kitten? What according to you should be the distance from the foot of the tree that will enable the fire fighters to rescue the kitten.

Answer 1

$\huge{\bold{\underline{\underline{Question:-}}}}$

A dog chases a kitten who starts climbing up a tree to protect itself from the dog. After climbing a height of 24 feet, it finds itself stuck and unable to climb down out of fear. Fire fighters are pressed into service to get the kitten down. But they have a problem. There ladder is 25 feet and they can go as close as 10 feet from the foot of the tree. Do you think at this distance, they will be able to rescue the kitten? What according to you should be the distance from the foot of the tree that will enable the fire fighters to rescue the kitten.

$\huge{\bold{\underline{\underline{Solution:-}}}}$

Height at which kitten are stuck = 24 feet

Height of ladder = 25 feet

distance from foot of tree = 10 feet

Let's assume that

• Point at which kitten is stuck be 'a'.
• Point at foot of tree be 'b'.
• Point where ladder is placed on the floor be 'c'.

Since, the ladder with respect to tree is forming a right angled triangle, so:-

By Pythagoras theorem :-

(AC)² = (AB)²+(BC)²

(25)² = (24)²+(10)²

625 = 576 + 100

625 ≠ 676

Since, they are not equal they will not be able to rescue the cat.

In order to rescue the cat, the required distance from the foot of tree the ladder should be placed is :-

(AC)² = (AB)²+(BC)²

(25)² = (24)²+(BC)²

625 = 576 + (BC)²

(BC)² = 625-576

(BC)² = 49

BC = √49

BC = 7

So, they should place the ladder 7 feet from foot of tree.

Hope it helps.............