a 20 foot latter will be used to paint the exterior of a house. The foot of the latter needs to be 4.5 feet from the base of the house. What is the maximum height the ladder will reach?
h^2 = 20^2 - 4.5^2
This is a problem for Pythagoras.
a^2 + b^2 = c^2
4.5^2 + b^2 = 20^2
20.25 + b^2 = 400
b^2 = 379.75
b = 19.5
To find the maximum height the ladder will reach, we can use the Pythagorean theorem, which states that in a right-angled 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, the distance from the base of the house to the foot of the ladder is one side, and the height of the ladder is the other side.
Let's denote the height of the ladder as 'h'. According to the problem, the distance from the base of the house to the foot of the ladder is 4.5 feet. We already know the length of the ladder is 20 feet.
Using the Pythagorean theorem, we can write the equation as:
h^2 = 20^2 - 4.5^2
Simplifying the equation:
h^2 = 400 - 20.25
h^2 = 379.75
To get the value of 'h', we need to find the square root of both sides of the equation:
h = √379.75
Calculating the square root, we find:
h ≈ 19.49
Therefore, the maximum height the ladder will reach is approximately 19.49 feet.