To find out how high the ladder reaches up the tree, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
In this case:
- The length of the ladder is the hypotenuse (\(c = 10\) feet).
- The distance from the base of the ladder to the tree is one leg of the triangle (\(a = 6\) feet).
- The height reached up the tree is the other leg (\(b\)).
According to the Pythagorean theorem: \[ a^2 + b^2 = c^2 \]
Substituting the values we know: \[ 6^2 + b^2 = 10^2 \] \[ 36 + b^2 = 100 \]
Now, solve for \(b^2\): \[ b^2 = 100 - 36 \] \[ b^2 = 64 \]
Taking the square root of both sides: \[ b = 8 \]
Thus, the height the ladder reaches up the tree is 8 feet.
The correct response is 8 feet.
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