Answer :
Let's solve the problem step-by-step:
1. To determine the distance from the wall to the bottom of the ladder along the horizontal ground, we can use the Pythagorean theorem. This theorem relates the lengths of the sides of a right triangle: [tex]\(a^2 + b^2 = c^2\)[/tex], where [tex]\(c\)[/tex] is the hypotenuse, [tex]\(a\)[/tex] is one leg, and [tex]\(b\)[/tex] is the other leg.
2. In this problem:
- The length of the ladder is the hypotenuse [tex]\(c = 100\)[/tex] cm.
- The height where the top of the ladder touches the wall is one leg [tex]\(a = 80\)[/tex] cm.
- We need to find the horizontal distance from the wall to the bottom of the ladder, which is the other leg [tex]\(b\)[/tex].
3. Applying the Pythagorean theorem:
[tex]\[
a^2 + b^2 = c^2 \implies 80^2 + b^2 = 100^2
\][/tex]
4. Calculate [tex]\(80^2\)[/tex] and [tex]\(100^2\)[/tex]:
[tex]\[
80^2 = 6400
\][/tex]
[tex]\[
100^2 = 10000
\][/tex]
5. Substitute these values back into the equation:
[tex]\[
6400 + b^2 = 10000
\][/tex]
6. Solve for [tex]\(b^2\)[/tex]:
[tex]\[
b^2 = 10000 - 6400
\][/tex]
[tex]\[
b^2 = 3600
\][/tex]
7. Find [tex]\(b\)[/tex] by taking the square root of both sides:
[tex]\[
b = \sqrt{3600}
\][/tex]
[tex]\[
b = 60
\][/tex]
So, the horizontal distance from the wall to the bottom of the ladder is [tex]\(60\)[/tex] cm.
Thus, the correct answer is:
C. 60 cm
1. To determine the distance from the wall to the bottom of the ladder along the horizontal ground, we can use the Pythagorean theorem. This theorem relates the lengths of the sides of a right triangle: [tex]\(a^2 + b^2 = c^2\)[/tex], where [tex]\(c\)[/tex] is the hypotenuse, [tex]\(a\)[/tex] is one leg, and [tex]\(b\)[/tex] is the other leg.
2. In this problem:
- The length of the ladder is the hypotenuse [tex]\(c = 100\)[/tex] cm.
- The height where the top of the ladder touches the wall is one leg [tex]\(a = 80\)[/tex] cm.
- We need to find the horizontal distance from the wall to the bottom of the ladder, which is the other leg [tex]\(b\)[/tex].
3. Applying the Pythagorean theorem:
[tex]\[
a^2 + b^2 = c^2 \implies 80^2 + b^2 = 100^2
\][/tex]
4. Calculate [tex]\(80^2\)[/tex] and [tex]\(100^2\)[/tex]:
[tex]\[
80^2 = 6400
\][/tex]
[tex]\[
100^2 = 10000
\][/tex]
5. Substitute these values back into the equation:
[tex]\[
6400 + b^2 = 10000
\][/tex]
6. Solve for [tex]\(b^2\)[/tex]:
[tex]\[
b^2 = 10000 - 6400
\][/tex]
[tex]\[
b^2 = 3600
\][/tex]
7. Find [tex]\(b\)[/tex] by taking the square root of both sides:
[tex]\[
b = \sqrt{3600}
\][/tex]
[tex]\[
b = 60
\][/tex]
So, the horizontal distance from the wall to the bottom of the ladder is [tex]\(60\)[/tex] cm.
Thus, the correct answer is:
C. 60 cm
