u7s1tfaq01A ladder 5 m long is placed against the side of a house so that it rests 4.2 m above the ground. How far is the base of the ladder from the base of the house?(Enter the number only to the nearest tenth.)
Question
u7s1tfaq01A ladder 5 m long is placed against the side of a house so that it rests 4.2 m above the ground. How far is the base of the ladder from the base of the house?(Enter the number only to the nearest tenth.)
Solution
This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, the ladder acts as the hypotenuse, the height from the ground to where the ladder touches the house is one side of the triangle, and the distance from the base of the house to the base of the ladder is the other side.
Given: Length of the ladder (hypotenuse, c) = 5 m Height from the ground to where the ladder touches the house (side a) = 4.2 m
We need to find the distance from the base of the house to the base of the ladder (side b).
According to the Pythagorean theorem:
c² = a² + b²
We can rearrange this to solve for b:
b² = c² - a²
Substituting the given values:
b² = 5² - 4.2² b² = 25 - 17.64 b² = 7.36
Taking the square root of both sides to solve for b:
b = √7.36 b = 2.7 m
So, the base of the ladder is approximately 2.7 m from the base of the house.
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