Question

A ladder of length 10cm placed against the wall and its top reaches the window at a height of 8m from the ground .find the distance between the foot of the ladder and the wall​

Answer 1

Answer :-

$\: \: \underline{\boxed{\sf{\blue{Let's \: understand \: the \: concept \: first}}}}$

We clearly see that here we have to find the Distance between the foot of ladder and wall. We know that wall is perpendicular to the land (assumed in maths) and ladder acts like its Hypotenuse. And base completes the third side of Triangle which here is the distance between the foot of the wall and ladder. So the easiest way is to apply Pythagoras Theorem here. This is given as :-

• (Hypotenuse)² = (Base)² + (Perpendicular)²

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★ Question :-

A ladder of length 10cm placed against the wall and its top reaches the window at a height of 8mfrom the ground. Find the distance between the foot of the ladder and the wall.

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★ Solution :-

Given,

$\: \: \: \: \sf{\purple{\Longrightarrow \: \: Height \: of \: the \: wall} \: = \: \orange{Perpendicular \: = \: 8 \: cm}}$

$\: \: \: \: \sf{\purple{\Longrightarrow \: \: Length \: of \: the \: ladder} \: = \: \orange{Hypotenuse \: = \: 10 \: cm}}$

$\: \: \: \: \rm{\green{\longrightarrow \: \: Let \: the \: distance \: between \: the \: foot \: of \: wall \: and \: foot \: of \: ladder \: be \: \underline{'Base'}}}$

Now by using Pythagoras theorem, we get,

➔ Hypotenuse² = Base² + Perpendicular²

➔ (10)² = (Base)² + (8)²

➔ 100 = Base² + 64

➔ (Base)² = 100 - 64

➔ Base² = 36

$\: \: \huge{\rm{\pink{\: \: \Longrightarrow \: \: Base \: = \: \sqrt{36} \: = 6}}}$

➔ Base of the triangle = 6 cm

$\: \: \underline{\boxed{\sf{\red{Hence, \: the \: distance \: between \: the \: foot \: of \: the \: ladder \: and \: the \: wall \: is \: \underline{6 \: cm}}}}}$

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$\: \: \underline{\rm{\mapsto \: \: \: Confused ? \: Don't \: worry \: let's \: check \: our \: answer}}$

In order to check our answer, we need to simply apply the values we got, into our equation. Then,

✰ Hypotenuse² = Base² + Perpendicular²

✰ (10)² = (6)² +

$\: \: \bf{\blue{\longrightarrow \: \: \: 10^{2} \: = \: 6^{2} \: + \: 8^{2}}}$

✰ 100 = 36 + 64

✰ 100 = 100

Clearly, LHS = RHS. So our answer is correct.

Hence, Verified.

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$\: \: \underline{\rm{\red{Evaluation \: of \: the \: figure \: :-}}}$

The figure is attached as an image. From that we get,

• Height of the wall = AB = Perpendicular = 8 cm

• Distance between the foot of wall and ladder = BC = Base = 6 cm

• Length of the ladder = AC = Hypotenuse = 10 cm

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$\: \: \underline{\boxed{\rm{\orange{Aid \: to \: the \: Memory \: :-}}}}$

• Pythagoras Theorem is the theorem was given by Pythagoras in early ADs.

• Pythagorean Triplet is the form of three numbers where the sum of the squares of two smaller number is equal to the square of the largest number. Here 6, 8 and 10 are Pythagorean Triplet.

• Trigonometry is the branch of mathematics that deals with the calculation of angle and lengths of side in a right angled triangle.

Answer 2

Answer:

Step-by-step explanation:

Given that:-

• Ladder of length 10 cm

• The window as support as 8m

• We need to find the distance

Concept:-

Pythagoras Theorem

Let's Do!

According to the Theorem,

The sum of the square of sides of a right angle Triangle is equal to square of its hypotenuse.

So, we need to find the Base.

$(8)^2+(Base)^2=(10)^2$

$64+(Base)^2= 100$

$(Base)^2= 100-64$

$(Base)^2= 36$

$Base= 6 \ cm$

So, 6 cm is the answer.

Note that only Pythagoras theorem is applicable. No other theorem can be used to determine the distances. Also, trigonometry can be used for the same.