A 12-foot ladder is set up 5 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.
To find out how far up the building the ladder reaches, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 acts as the hypotenuse, the distance from the base of the building to the ladder is one side, and the distance up the building is the other side.
Let's label the distance up the building as "x". Applying the Pythagorean theorem, we have:
x^2 + 5^2 = 12^2
Simplifying this equation, we get:
x^2 + 25 = 144
Subtracting 25 from both sides:
x^2 = 119
Taking the square root of both sides to solve for x:
x = √119
Using a calculator, we find that √119 is approximately 10.9.
Therefore, the ladder reaches approximately 10.9 feet up the building.
To find out how far up the building the ladder reaches, we can use the Pythagorean theorem. The theorem 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 is the hypotenuse, and we have the length of the base (5 feet) and the length of the ladder (12 feet). Let's call the distance up the building that the ladder reaches "x".
So, according to the Pythagorean theorem, we have:
x^2 + 5^2 = 12^2
Simplifying the equation, we get:
x^2 + 25 = 144
Subtracting 25 from both sides, we have:
x^2 = 119
Taking the square root of both sides, we get:
x ≈ 10.9
Therefore, the ladder reaches approximately 10.9 feet up the building.