To find out how high the ladder reaches up the tree using the Pythagorean theorem, we can think of the situation as a right triangle where:
- The ladder is the hypotenuse (20 feet),
- The distance from the base of the ladder to the tree is one leg (12 feet),
- The height that the ladder reaches up the tree is the other leg, which we will call \( h \).
According to the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where
- \( a \) is one leg (12 feet),
- \( b \) is the other leg (the height \( h \)),
- \( c \) is the hypotenuse (20 feet).
Plugging in the values, we have:
\[ 12^2 + h^2 = 20^2 \]
Calculating the squares:
\[ 144 + h^2 = 400 \]
Now, solve for \( h^2 \):
\[ h^2 = 400 - 144 \] \[ h^2 = 256 \]
Now, take the square root of both sides to find \( h \):
\[ h = \sqrt{256} = 16 \]
Thus, the height that the ladder reaches up the tree is 16 feet.
The correct response is 16 feet.
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