Question
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
15 feet
16 feet
17 feet
18 feet
Answers
Bot
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.
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.