Question

A pole of 17 m rests on a wall at a
hight of 15 m. Suddenly it starts
Sliding down and rests at a hight of 8m.
Find the resting point of the foot on the
ground in both cases?​

Answer 1

Given :-

▪ A pole of length 17 m rests on a wall at a height of 15 m. Suddenly it started sliding down and stops at a height of 8m.

To Find :-

▪ The resting point of the foot on the ground in both cases.

Solution :-

Imagine the length of pole and the height at which is it put to be Hypotenuse and Perpendicular of a hypothetical right triangle.

So, Using Pythagoras theorem, we have

⇒ Hypotenuse² = Base² + Height²

⇒ (17)² = Base² + (15)²

⇒ Base² = 289 - 225

⇒ Base = 6 m [ Negative length is not possible ]

So, In the first case (Before sliding of the pole) the resting point is 6 m.

Now, In the second case the pole slided down and stopped at a height of 8 m. Imagine it as the same hypothetical right triangle but with different height and different base, Obviously.

But the length of the pole is constant. That means the Hypotenuse is 17 m.

Using the Pythagoras theorem, we have

⇒ Hypotenuse² = Base² + Perpendicular²

⇒ 289 - 64 = Base²

⇒ Base = 15 m

Hence, In this case the resting point of the pole on the foot is 15 m .

Answer 2

★ QUESTION :

A pole of 17m rests on a wall at a height of 15m. Suddenly it starts sliding down and rests at a height of 8m. Find the resting point of the food on the ground in both cases ?

GIVEN :

• Pole in rest (metres) = 17m
• Height of the pole at rest on the wall = 15m
• (Sliding down and rest) at a height = 8m

TO FIND :

• The resting point in both the cases = ?

STEP -BY-STEP EXPLAINATION :

As per the provided question we have to find resting point of of the food on the ground in both cases, therefore before finding we will have to see the given parts and work according to appropriate formulas that is to be applied :

The provided information shows that :

⟼ Pole in rest (metres) = 17 m

⟼Height of the pole at rest = 15 m

⟼(Sliding down and rest) at height = 8 m

Now, we will have to use the Pythagoras theorem so, that we can go to the next process for finding our appropriate answer –

━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore, we are finding here resting point of the foot on the ground (In First case) :

Formula applied for Pythagoras theorem :

➠ Hypotenuse² = Base² + Height²

[ Substituting the values as per the formula ]

➠ (17)² = Base² + (15)²

➠ Base² = (17)² - (15)²

➠ Base² = 289 - 225

➠ Base = 6m

━━━━━━━━━━━━━━━━━━━━━━━━━

Now, we will find here resting point of the foot on the ground (In Second Case) :

Therefore, here we can simply find that – 'when the pole is slided' height is given as 8m and length of the pole is as usual Therefore, hypotenuse will be 17m. So, now here we will use the formula of (Pythagoras theorem) that's why because we will find here resting point of the pole = ? [(so let us begin it )]

Formula of Pythagoras theorem :

⟹ Hypotenuse² = Base² + Perpendicular²

[ Substituting the values as Per Formula ]

⟹ 289 - 64 = Base²

⟹ Base² = 289 - 64

⟹ Base = 15m

Therefore, the resting point of the foot on the ground ground = 15m