If the base to a gutter and 12 feet from the base of a house, how many feet high on the house does the ladder reachIf th
To find out how high on the house the ladder reaches, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the two legs (the sides adjacent to the right angle) is equal to the square of the hypotenuse (the side opposite the right angle, which is the ladder in this case).
Let's assign variables to the lengths involved:
- Let the height on the house reached by the ladder be represented by 'h' (in feet).
- Let the base of the gutter be represented by 'b' (in feet).
- Let the distance from the base of the house to the gutter be represented by 'd' (in feet).
In this scenario:
- The ladder acts as the hypotenuse of a right triangle.
- The base of the gutter acts as one of the legs.
- The distance from the base of the house to the gutter constitutes the other leg.
Therefore, we have the following right triangle:
|\
| \
h | \
| \
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b d
Using the Pythagorean Theorem, we can form an equation:
b^2 + d^2 = h^2
Now, we can substitute the given values into this equation and solve for 'h':
b = length of the base of the gutter = given as unknown
d = distance from the base of the house to the gutter = 12 feet
b^2 + d^2 = h^2
Plugging in the known values:
b^2 + 12^2 = h^2
Simplifying the equation:
b^2 + 144 = h^2
Since we don't have the length of the gutter base, we cannot determine the exact measurement of 'h' (the height on the house reached by the ladder) without that information. However, once we know the length of the gutter base, we can substitute it into the equation and solve for 'h'.