A 12 - ft ladder leans against the side of a house. The bottom of the ladder is 6 ft from the side of the house. How high is the top of the ladder from the ground? If necessary, round your answer to the nearest tenth.
10.4
Well, if a 12-ft ladder leans against a house, we can assume it's having a "ladder-y" day! Now, to find out how high the top of the ladder is from the ground, we can use a little bit of Pythagorean magic!
We have a right triangle here where the ladder is the hypotenuse, and the distance from the house to the bottom of the ladder is one of the legs. The other leg is the height we're looking for.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can plug in the values:
(6^2) + (b^2) = (12^2)
36 + b^2 = 144
b^2 = 144 - 36
b^2 = 108
Now, let's put on our math clown wig and solve for b:
b = √108 ≈ 10.4
So, the top of the ladder is approximately 10.4 feet from the ground. Keep in mind that I rounded my answer to the nearest tenth, just like a circus clown balancing on a tightrope!
To find out how high the top of the ladder is from the ground, 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, and the distance from the house to the bottom of the ladder forms one of the legs. So, we can use the Pythagorean theorem to solve for the other leg, which represents the height of the ladder.
Let's denote the height of the ladder as h. According to the problem, the bottom of the ladder is 6 ft from the side of the house, so the other leg of the right triangle is 6 ft.
Now, we can use the Pythagorean theorem:
hypotenuse^2 = leg1^2 + leg2^2
12^2 = 6^2 + h^2
144 = 36 + h^2
h^2 = 144 - 36
h^2 = 108
To solve for h, we take the square root of both sides:
h = √108
Using a calculator, the square root of 108 is approximately 10.4 (rounded to the nearest tenth).
Therefore, the top of the ladder is approximately 10.4 ft from the ground.
To find the height of the ladder, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the ladder, the side of the house, and the ground form a right triangle. The ladder is the hypotenuse, and its length is given as 12 ft. The distance from the house to the ladder forms one leg of the triangle and is given as 6 ft. Let's call the height of the ladder (the distance from the ground to the top of the ladder) "h."
We can set up the equation using the Pythagorean theorem:
12^2 = 6^2 + h^2
Simplifying:
144 = 36 + h^2
Subtracting 36 from both sides:
108 = h^2
Taking the square root of both sides:
√108 = h
Now, to find the decimal approximation, we can use a calculator to evaluate √108.
√108 ≈ 10.39
Therefore, the top of the ladder is approximately 10.4 ft from the ground.
this is the Pythagorean Theorem
the ladder is the hypotenuse of a right triangle
(height)^2 = 12^2 - 6^2