A ladder is leaning against a house. the distance from the top of the ladder to the ground is 12 feet, and the distance from the foot of the ladder to the house is 4 feet. how tall is the ladder?
a^2 + b^2 = c^2
12^2 + 4^2 = c^2
144 + 16 = c^2
160 = c^2
12.65 = c
thank you
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To find the height of the ladder, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms a right-angled triangle with the ground and the side of the house. The distance from the top of the ladder to the ground (12 feet) is the length of the hypotenuse, and the distance from the foot of the ladder to the house (4 feet) is one of the other two sides.
Using the Pythagorean theorem, we have:
hypotenuse^2 = side1^2 + side2^2
where:
hypotenuse = length of the ladder
side1 = distance from the top of the ladder to the ground
side2 = distance from the foot of the ladder to the house
Substituting the given values into the equation, we have:
ladder^2 = 12^2 + 4^2
Simplifying:
ladder^2 = 144 + 16
ladder^2 = 160
To solve for the length of the ladder, we need to take the square root of both sides:
ladder = √160
ladder ≈ 12.65 feet
Therefore, the ladder is approximately 12.65 feet tall.