a 9 ft ladder is leaning against a wall so that Adam can hang a picture 7.5 ft above the floor. how far does the ladder need to be placed from the wall?
a^2 + b^2 = c^2
7.5^2 + b^2 = 9^2
56.25 + b^2 = 81
b^2 = 81 - 56.25
b^2 = 24.75
b = 4.795 feet
thank u
You're welcome.
To find out how far the ladder needs to be placed from the wall, we can use the Pythagorean theorem. The theorem 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 other two sides. In this case, the ladder is the hypotenuse, so we need to find the length of the other two sides (the distance from the wall and the height of the picture).
Let's assign variables:
- The distance from the wall to the ladder's base: let's call it 'x'.
- The height of the picture: 7.5 ft
- The length of the ladder: 9 ft
Now we can use the Pythagorean theorem to set up the equation:
x^2 + 7.5^2 = 9^2
Simplifying the equation:
x^2 + 56.25 = 81
Subtracting 56.25 from both sides:
x^2 = 24.75
To find 'x', we need to take the square root of both sides:
x = √24.75
Calculating the square root of 24.75:
x ≈ 4.975
Therefore, the ladder needs to be placed approximately 4.975 ft away from the wall.