# A 15m long ladder reached a window 12m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.

Answer

Verified

327k+ views

Hint: Wall and ground are always perpendicular to each other. So, let us apply Pythagoras theorem to find the value of a.

Complete step-by-step answer:

Now as referenced from the given figure that,

The distance of the window from the ground is 12 m (AB = 12 m).

And, the length of the ladder is 15 m (AC = 15 m).

Now as we know that walls and ground are always perpendicular to each other.

So, ABC triangle formed would be a right-angled triangle, right-angled at B and the hypotenuse of the triangle ABC will be the side opposite to the right angle (i.e. AC).

So, we can apply the Pythagorean theorem in the triangle ABC.

According to Pythagoras theorem, if XYZ is any right-angled triangle, right-angled at Y. And XZ is the hypotenuse of triangle XYZ.

Then, \[{\left( {{\text{XZ}}} \right)^{\text{2}}}{\text{ = }}{\left( {{\text{XY}}} \right)^{\text{2}}}{\text{ + }}{\left( {{\text{YZ}}} \right)^{\text{2}}}\]

So, applying Pythagoras theorem in triangle ABC. We get,

\[{\left( {{\text{AC}}} \right)^{\text{2}}}{\text{ = }}{\left( {{\text{AB}}} \right)^{\text{2}}}{\text{ + }}{\left( {{\text{BC}}} \right)^{\text{2}}}\] (1)

Now we had to find the value of BC using equation 1.

\[{\left( {{\text{BC}}} \right)^{\text{2}}}{\text{ = }}{\left( {{\text{AC}}} \right)^{\text{2}}}{\text{ - }}{\left( {{\text{AB}}} \right)^{\text{2}}}\]

Now putting the value of AC and AB in the above equation. We get,

\[{\left( {{\text{BC}}} \right)^{\text{2}}}{\text{ = }}{\left( {15} \right)^{\text{2}}}{\text{ - }}{\left( {12} \right)^{\text{2}}}{\text{ }} = {\text{ }}225{\text{ }} - {\text{ }}144{\text{ }} = {\text{ }}81\]

Now, taking the square root of both sides of the above equation. We get,

BC = 9 m (Because distance cannot be negative)

Hence, the distance of the foot of the ladder from the wall is 9m.

Note: Whenever we come up with a type of problem then first, we check whether there was any angle given between two lines (like ladder or walls). Then after that if the angle is \[{90^0}\] then the best way to find the distance is by using the Pythagorean theorem in a right-angled triangle.

Complete step-by-step answer:

Now as referenced from the given figure that,

The distance of the window from the ground is 12 m (AB = 12 m).

And, the length of the ladder is 15 m (AC = 15 m).

Now as we know that walls and ground are always perpendicular to each other.

So, ABC triangle formed would be a right-angled triangle, right-angled at B and the hypotenuse of the triangle ABC will be the side opposite to the right angle (i.e. AC).

So, we can apply the Pythagorean theorem in the triangle ABC.

According to Pythagoras theorem, if XYZ is any right-angled triangle, right-angled at Y. And XZ is the hypotenuse of triangle XYZ.

Then, \[{\left( {{\text{XZ}}} \right)^{\text{2}}}{\text{ = }}{\left( {{\text{XY}}} \right)^{\text{2}}}{\text{ + }}{\left( {{\text{YZ}}} \right)^{\text{2}}}\]

So, applying Pythagoras theorem in triangle ABC. We get,

\[{\left( {{\text{AC}}} \right)^{\text{2}}}{\text{ = }}{\left( {{\text{AB}}} \right)^{\text{2}}}{\text{ + }}{\left( {{\text{BC}}} \right)^{\text{2}}}\] (1)

Now we had to find the value of BC using equation 1.

\[{\left( {{\text{BC}}} \right)^{\text{2}}}{\text{ = }}{\left( {{\text{AC}}} \right)^{\text{2}}}{\text{ - }}{\left( {{\text{AB}}} \right)^{\text{2}}}\]

Now putting the value of AC and AB in the above equation. We get,

\[{\left( {{\text{BC}}} \right)^{\text{2}}}{\text{ = }}{\left( {15} \right)^{\text{2}}}{\text{ - }}{\left( {12} \right)^{\text{2}}}{\text{ }} = {\text{ }}225{\text{ }} - {\text{ }}144{\text{ }} = {\text{ }}81\]

Now, taking the square root of both sides of the above equation. We get,

BC = 9 m (Because distance cannot be negative)

Hence, the distance of the foot of the ladder from the wall is 9m.

Note: Whenever we come up with a type of problem then first, we check whether there was any angle given between two lines (like ladder or walls). Then after that if the angle is \[{90^0}\] then the best way to find the distance is by using the Pythagorean theorem in a right-angled triangle.

Last updated date: 06th Jun 2023

â€¢

Total views: 327k

â€¢

Views today: 2.83k

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India