20'ladder placed 5'from base of house. How high up ladder reach?
a^2 + b^2 = c^2
5^2 + b^2 = 20^2
25 + b^2 = 400
b^2 = 375
b = 19.36
To find out how high up the ladder will reach, you need to 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 acts as the hypotenuse, the distance of the ladder from the base of the house acts as one side, and the height the ladder reaches acts as the other side. Let's label these sides:
Base of the ladder from the house = 5 feet
Height the ladder reaches = ?
Hypotenuse (length of the ladder) = 20 feet
Using the Pythagorean theorem, we can set up the equation:
(5 feet)^2 + (height)^2 = (20 feet)^2
Now we can solve for the height the ladder reaches:
25 + (height)^2 = 400
Subtract 25 from both sides:
(height)^2 = 375
Take the square root of both sides to find the height:
height ≈ √375 ≈ 19.36 feet
Therefore, the ladder will reach a height of approximately 19.36 feet.