A 25 ft. Ladder is placed 8 ft. From the base of the house. How high up the side of the house can the ladder reach?
Use the Pythagorean Theorem.
8^2 + b^2 = 25^2
64 + b^2 = 625
b^2 = 561
b = 23.69 feet
A garden is in the shape of a right triangle. One leg of the triangle is 5 feet long, and the hypotenuse is 10 feet long. To the nearest tenth of a foot, how long is the other leg?
To find out how high up the side of the house the ladder can reach, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder is the hypotenuse and the distance from the base of the house to the ladder forms one side of the right triangle. The height up the side of the house that the ladder can reach is the other side of the right triangle.
Let's denote the height up the side of the house as "h". According to the Pythagorean theorem, we have:
h^2 = L^2 - d^2
where L is the length of the ladder and d is the distance from the base of the ladder to the house.
Plugging in the values, we get:
h^2 = 25^2 - 8^2
h^2 = 625 - 64
h^2 = 561
To find the value of "h", we take the square root of both sides:
h = √561
Calculating this value, we find that the ladder can reach approximately 23.66 feet up the side of the house.
To find out how high up the side of the house the ladder can reach, 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 represents the hypotenuse, the distance from the base of the house represents one of the other sides, and the height up the side of the house represents the remaining side.
Let's call the height up the side of the house "h," the distance from the base of the house "d," and the length of the ladder "L." According to the Pythagorean theorem, we have the equation:
L^2 = d^2 + h^2
We are given that the distance from the base of the house is 8 ft, which means d = 8 ft, and the length of the ladder is 25 ft, which means L = 25 ft. Our equation becomes:
25^2 = 8^2 + h^2
625 = 64 + h^2
Subtracting 64 from both sides, we get:
625 - 64 = h^2
561 = h^2
To find the height up the side of the house, we need to take the square root of both sides:
√561 ≈ 23.69
Therefore, the ladder can reach approximately 23.69 ft up the side of the house.