Question

A ladder 17m long,reaches a window of a building 15m above the ground. Find the distance of the foot of the ladder from the building.​

Answer 1

Given:

A ladder 17m long, reaches a window of a building 15m above the ground.

To find:

The distance of the foot of the ladder from the building.

Concept:

Here the concept of Pythagoras Theorem will be used.

The Pythagoras theorem states that if a triangle is right-angled, then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

$\boxed{H^2 = P^2 + B^2}$

Where, $H$ is hypotenuse, $P$ is perpendicular and $B$ is base of the right angled triangle.

Calculation:

We know that, building is always perpendicular to ground.

Hence, the ladder building and ground will form a right angled triangle with the wall hypotenuse 17m and perpendicular 15m.

We are supposed to find the third side of the ladder building.

Let $x$ be the third side of the ladder building.

We can find the third side of the ladder building, using the Pythagoras theorem.

The Pythagoras theorem states that if a triangle is right-angled, then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

$H^2 = P^2 + B^2$

Here, we have to find the base of the ladder building, i.e., third side of the ladder building.

So, on substituting the given values in the formula, we get:

$\implies (17)^2 = (15)^2 + x^2 \\ \\ \implies 289 = 225 + x^2 \\ \\ \implies 289 - 225 = x^2 \\ \\ \implies 64 = x^2 \\ \\ \implies x = \sqrt{64} \\ \\ \implies \boxed{x = 8}$

Hence, the distance of the ladder from the building is 8cm.

Answer 2

Question :-

• A ladder 17 m long, reaches a window of a building 15 m above the ground . Find the Distance of the foot of the ladder from the building .

Answer :-

• The distance of the foot of the ladder from the building is 8 meter .

Explanation :-

● In the above diagram :-

• AB is the distance of the window from the wall .
• AC is the length of the ladder .
• BC is the segment, which we need to find .

We assumed that ,

• $\sf{\angle ABC = 90 \degree}$

∴ By using Pythagoras Theorem :-

$\Longrightarrow \: \: \sf{(Hypotenuse) {}^{2} = (Side \: 1) {}^{2} + (Side \: 2) {}^{2} }$

Here ,

• Hypotenuse = AC
• Side 1 = AB
• Side 2 = BC

∴ By substituting the given values :-

$\Longrightarrow \: \: \sf{(AC) { }^{2} = (AB) {}^{2} + (AC) {}^{2} }$

$\Longrightarrow \: \: \sf{(17) {}^{2} = (15) {}^{2} + (x) {}^{2} }$

$\Longrightarrow \: \: \sf{x {}^{2} = 17 {}^{2} - 15 {}^{2} }$

$\Longrightarrow \: \: \sf{ {x}^{2} \: = \: 64}$

$\Longrightarrow \: \: \sf{x \: = \: \sqrt{64} }$

$\Longrightarrow \: \: \sf{x \: = \: 8 \: meter}$

Hence :-

• Distance = 8 meter .

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Note :- All measurements are in meter .