A ladder base is 3 m away from a house, and the fully extended ladder is 5 m long when it leans against the house. How high does the ladder reach on the house?
It makes a right-angle triangle.
a^2 + b^2 = c^2
3^2 + b^2 = 5^2
9 + b^2 = 25
b^2 = 16
b = 4 meters
Thank you so very much
To determine how high the ladder reaches on the house, we can use the Pythagorean theorem, which states that in a right-angled 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 distance from the base of the ladder to the house forms the base of the right-angled triangle, and the ladder itself serves as the hypotenuse. The height to which the ladder reaches on the house represents the other side of the triangle.
Let's denote the height of the ladder on the house as 'h,' the distance from the base of the ladder to the house as 'b,' and the length of the ladder as 'l'.
According to the given information, we have:
b = 3 m
l = 5 m
We can use the Pythagorean theorem to solve for 'h':
l^2 = b^2 + h^2
Substituting the known values:
(5 m)^2 = (3 m)^2 + h^2
25 m^2 = 9 m^2 + h^2
25 m^2 - 9 m^2 = h^2
16 m^2 = h^2
To find 'h,' we take the square root of both sides of the equation:
√(16 m^2) = √(h^2)
4 m = h
Therefore, the ladder reaches a height of 4 meters on the house.