Marvin has a 27-foot ladder. Safety standards dictate that the base of a 27-foot ladder should be placed 7 feet from a vertical wall.
How far above the ground will the top of the ladder be on the wall, in feet? Round your answer to the nearest hundredth.
a^2 + b^2 = c^2
a^2 + 7^2 = 27^2
a^2 + 49 = 729
a^2 = 680
a = 26.08
To find out how far above the ground the top of the ladder will be on the wall, we can use the Pythagorean theorem. The Pythagorean 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 represents the hypotenuse of a right triangle, and the distance from the base of the ladder to the wall represents one of the sides.
Let's call the distance from the base of the ladder to the wall "x". According to the safety standards, x is equal to 7 feet.
We can use the Pythagorean theorem to find the height of the ladder on the wall. The equation is: x^2 + h^2 = 27^2.
Substituting the value of x, we have: 7^2 + h^2 = 27^2.
Simplifying the equation: 49 + h^2 = 729.
To solve for h, we need to isolate the variable. Subtracting 49 from both sides: h^2 = 680.
Taking the square root of both sides to find h, we get: h ≈ √680 ≈ 26.08.
Therefore, the top of the ladder will be approximately 26.08 feet above the ground on the wall. Rounded to the nearest hundredth, the answer is 26.08 feet.