Sure, let's solve this step-by-step.
We are dealing with a right triangle formed by the ladder, the wall, and the ground. Here is what we know:
- The ladder serves as the hypotenuse of the triangle.
- The horizontal distance from the foot of the ladder to the wall is one of the legs of the triangle.
- We need to find the height up the wall where the ladder touches, which is the other leg of the triangle.
Given:
1. The length of the ladder (hypotenuse, [tex]\( c \)[/tex]) is [tex]\( 17 \)[/tex] meters.
2. The horizontal distance from the wall (one leg, [tex]\( b \)[/tex]) is [tex]\( 8 \)[/tex] meters.
We will use the Pythagorean theorem to find the height [tex]\( a \)[/tex]. The Pythagorean theorem states:
[tex]\[ a^2 + b^2 = c^2 \][/tex]
Rearranging to solve for [tex]\( a \)[/tex]:
[tex]\[ a^2 = c^2 - b^2 \][/tex]
Now, substitute the given values:
[tex]\[ a^2 = 17^2 - 8^2 \][/tex]
[tex]\[ a^2 = 289 - 64 \][/tex]
[tex]\[ a^2 = 225 \][/tex]
Taking the square root of both sides to find [tex]\( a \)[/tex]:
[tex]\[ a = \sqrt{225} \][/tex]
[tex]\[ a = 15 \][/tex]
So, the ladder reaches [tex]\( 15 \)[/tex] meters up the wall.
