Question
A ladder 6 m long reaches 5.2 m up a wall .How far is the foot of the ladder from the base of the wall?
Answers
GPT-4o mini
To find the distance from the foot of the ladder to the base of the wall, we can use the Pythagorean theorem. The ladder, the wall, and the ground form a right triangle, where:
- The length of the ladder is the hypotenuse (6 m).
- The height reached up the wall is one leg of the triangle (5.2 m).
- The distance from the foot of the ladder to the base of the wall is the other leg of the triangle (let's call it \( x \)).
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs of the triangle, and \( c \) is the length of the hypotenuse. Plugging in our values:
\[
x^2 + 5.2^2 = 6^2
\]
Calculating \( 5.2^2 \) and \( 6^2 \):
\[
x^2 + 27.04 = 36
\]
Now, subtract \( 27.04 \) from both sides:
\[
x^2 = 36 - 27.04
\]
\[
x^2 = 8.96
\]
Now, take the square root of both sides to find \( x \):
\[
x = \sqrt{8.96} \approx 2.99 \text{ m}
\]
So, the foot of the ladder is approximately **2.99 meters** from the base of the wall.
- The length of the ladder is the hypotenuse (6 m).
- The height reached up the wall is one leg of the triangle (5.2 m).
- The distance from the foot of the ladder to the base of the wall is the other leg of the triangle (let's call it \( x \)).
According to the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where \( a \) and \( b \) are the lengths of the legs of the triangle, and \( c \) is the length of the hypotenuse. Plugging in our values:
\[
x^2 + 5.2^2 = 6^2
\]
Calculating \( 5.2^2 \) and \( 6^2 \):
\[
x^2 + 27.04 = 36
\]
Now, subtract \( 27.04 \) from both sides:
\[
x^2 = 36 - 27.04
\]
\[
x^2 = 8.96
\]
Now, take the square root of both sides to find \( x \):
\[
x = \sqrt{8.96} \approx 2.99 \text{ m}
\]
So, the foot of the ladder is approximately **2.99 meters** from the base of the wall.