Bob placed a 17-foot ramp against the side of a house so the ramp rested on a ledge that is 8 feet above the ground. How far was the base of the ramp from the house?
15 feet
16 feet
17 feet
18 feet
By using the Pythagorean theorem, we can find the distance between the base of the ramp and the house.
Let x be the distance between the base of the ramp and the house.
According to the Pythagorean theorem, in a right triangle with legs of length a and b and hypotenuse of length c, the equation is given by:
a^2 + b^2 = c^2
In this case, the height of the ledge (a) is 8 feet, and the length of the ramp (c) is 17 feet. We need to find the length of the base of the ramp (b).
Plugging in the values into the equation:
x^2 + 8^2 = 17^2
x^2 + 64 = 289
x^2 = 289 - 64
x^2 = 225
Taking the square root of both sides:
x = √225
x = 15
Therefore, the base of the ramp is 15 feet from the house.
The correct answer is 15 feet.
To find the distance between the base of the ramp and the house, we can use the Pythagorean theorem.
According to the theorem, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the ramp, and the other two sides are the height of the ledge and the distance between the base of the ramp and the house.
Using the Pythagorean theorem:
(hypotenuse)^2 = (height)^2 + (distance)^2
Substituting the given values:
(17 feet)^2 = (8 feet)^2 + (distance)^2
Simplifying the equation:
289 = 64 + (distance)^2
289 - 64 = (distance)^2
225 = (distance)^2
Taking the square root of both sides:
distance =√225
distance =15 feet
Therefore, the base of the ramp is 15 feet from the house.