a 13 ft ladder is placed against a vertical wall of a building, with the bottom of the ladder stand on level ground 5ft from the base of the building. how high up the wall does the ladder reach.
Well, let's see. It seems like we have quite the situation here. A 13-foot ladder against a vertical wall, with its bottom 5 feet away from the base of the building. I must say, that's quite a precarious position for a ladder to be in. It's as if the ladder is playing a dangerous game of "Will I Reach The Top?"
Now, if we were to analyze this situation with all seriousness (which, by the way, is not really my forte), we can use a little math. According to good ol' Pythagoras, the sum of the squares of the ladder's base and height is equal to the square of the ladder's hypotenuse. So, let's calculate!
The base of the ladder is 5 feet away from the base of the building. The ladder itself is 13 feet long. Now, if we imagine that the ladder, the wall, and the ground form a lovely right-angled triangle, we can use the Pythagorean theorem to solve for the height.
In this case, since the ladder is the hypotenuse, we have:
hypotenuse² = base² + height²
Plugging in the numbers, we have:
13² = 5² + height²
That simplifies to:
169 = 25 + height²
Subtracting 25 from both sides, we get:
144 = height²
Taking the square root of both sides:
height ≈ 12
So, it seems like the ladder reaches a height of approximately 12 feet up the wall. Yep, just high enough for all those hard-to-reach spots and a little extra for good measure. Just remember, ladders and walls make a good team, but don't forget your safety helmet and clown makeup! Safety first, always!
I hope that answers your question in a somewhat informative and humorous way! Let me know if there's anything else I can help you with.
To find the height the ladder reaches on the wall, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse, which in this case is the ladder, is equal to the sum of the squares of the other two sides.
In this case, one of the sides is the distance between the base of the building and the bottom of the ladder, which is 5ft. Let's call this side "a."
The other side is the height the ladder reaches on the wall. Let's call this side "b."
The ladder itself is the hypotenuse of the triangle. Let's call the length of the ladder "c." In this case, the length of the ladder is 13ft.
Let's put this information into the Pythagorean theorem equation:
a^2 + b^2 = c^2
Plugging in the values we know:
5^2 + b^2 = 13^2
25 + b^2 = 169
Now, let's solve for b:
b^2 = 169 - 25
b^2 = 144
Taking the square root of both sides:
b = √144
b = 12
Therefore, the ladder reaches a height of 12ft on the wall.
To find out how high up the wall the ladder reaches, we can use the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the other two sides.
In this scenario, one side of the right triangle is the height of the wall, the other side is the distance between the base of the ladder and the building, and the hypotenuse is the length of the ladder.
Let's use the formula:
a^2 + b^2 = c^2
where:
a = distance between the base of the ladder and the building (5 ft)
c = length of the ladder (13 ft)
b = height of the wall (unknown)
Plugging in the known values, we have:
5^2 + b^2 = 13^2
25 + b^2 = 169
Now, solve for b:
b^2 = 169 - 25
b^2 = 144
Taking the square root of both sides:
b = √144
b = 12
Therefore, the ladder reaches 12 feet up the wall.
The ladder is the hypotenuse of a right triangle.
a^2 + b^2 = c^2
5^2 + b^2 = 13^2
25 + b^2 = 169
b^2 = 144
b = 12