A ladder leans against the side of a house. The top of the ladder is 12 ft from the ground. The bottom of the ladder is 7 ft from the side of the house. Find the length of the ladder. If necessary, round your answer to the nearest tenth.
Pythagorean theorem:
b^2 + h^2 = 7^2 + 12^2 = L^2
To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square 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 the hypotenuse of a right triangle, with the ground and the side of the house forming the other two sides.
Let's call the length of the ladder "c", the distance from the ground to the top of the ladder "a", and the distance from the bottom of the ladder to the side of the house "b".
According to the information given, we have:
a = 12 ft (distance from the ground to the top of the ladder)
b = 7 ft (distance from the bottom of the ladder to the side of the house)
Using the Pythagorean theorem:
c^2 = a^2 + b^2
Substituting in the given values:
c^2 = 12^2 + 7^2
c^2 = 144 + 49
c^2 = 193
To find the length of the ladder, we need to take the square root of both sides:
c = √(193)
Rounding to the nearest tenth:
c ≈ 13.9 ft
Therefore, the length of the ladder is approximately 13.9 feet.