A building is 2 ft from a 9-ft fence that surrounds the property. Worker wants to wash window in the building 13 ft from the ground. He wants to place ladder over fence so it rests against the building. He decides he should place the ladder 8 ft from the fence for stability. to nearest tenth of foot, how long does ladder need to be?
It helps to draw a picture. You can ignore the length of the fence, add 2 to 8 to get the length of the one leg of the triangle (the other is 13), and use the formula a^2 + b^2 = c^2
Thanks. I tried that, but am still not getting the book answer of 16 ft 4 inches.
The book could be wrong. The wording is a little confusing too.
To determine the length of the ladder needed, we can use the Pythagorean theorem. According to the problem, the ladder forms a right triangle with the ground and the side of the building.
The two legs of the right triangle are:
1. The distance from the base of the ladder to the fence, which is 2 ft.
2. The height from the base of the ladder to the window, which is 13 ft.
The length of the ladder, which represents the hypotenuse of the right triangle, can be found by using the Pythagorean theorem:
a^2 + b^2 = c^2
Where:
a = the length of the first leg (2 ft)
b = the length of the second leg (13 ft)
c = the length of the hypotenuse (length of the ladder)
Let's plug in the given values:
2^2 + 13^2 = c^2
4 + 169 = c^2
173 = c^2
To find c, we take the square root of both sides:
c = √173
Using a calculator, we find that the square root of 173 is approximately 13.152.
Therefore, the ladder needs to be approximately 13.2 feet long when rounded to the nearest tenth of a foot.