Emaniee would like to build a ramp for her dog over some stairs.
1. Compute the distance between points B and C and enter it on the worksheet
right triangle: 30 inches, 7 inches, 11 inches
To compute the distance between points B and C, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is the distance between points B and C, which we want to find. The other two sides are 30 inches and 7 inches.
Applying the Pythagorean theorem, we have:
hypotenuse^2 = 30^2 + 7^2
hypotenuse^2 = 900 + 49
hypotenuse^2 = 949
Taking the square root of both sides, we find:
hypotenuse = √949
hypotenuse ≈ 30.82 inches
Therefore, the distance between points B and C is approximately 30.82 inches.
now calculate the distance between A and B please
To calculate the distance between points A and B, we can again use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is the distance between points A and B, which we want to find. The other two sides are 11 inches and 7 inches.
Applying the Pythagorean theorem, we have:
hypotenuse^2 = 11^2 + 7^2
hypotenuse^2 = 121 + 49
hypotenuse^2 = 170
Taking the square root of both sides, we find:
hypotenuse = √170
hypotenuse ≈ 13.04 inches
Therefore, the distance between points A and B is approximately 13.04 inches.
do D and B now
To calculate the distance between points D and B, we can again use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is the distance between points D and B, which we want to find. The other two sides are 30 inches and 11 inches.
Applying the Pythagorean theorem, we have:
hypotenuse^2 = 30^2 + 11^2
hypotenuse^2 = 900 + 121
hypotenuse^2 = 1021
Taking the square root of both sides, we find:
hypotenuse = √1021
hypotenuse ≈ 31.96 inches
Therefore, the distance between points D and B is approximately 31.96 inches.
now D and C
To calculate the distance between points D and C, we can again use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is the distance between points D and C, which we want to find. The other two sides are 30 inches and 13.04 inches (the distance between A and B, which we previously calculated).
Applying the Pythagorean theorem, we have:
hypotenuse^2 = 30^2 + 13.04^2
hypotenuse^2 = 900 + 170.2716
hypotenuse^2 = 1070.2716
Taking the square root of both sides, we find:
hypotenuse = √1070.2716
hypotenuse ≈ 32.72 inches
Therefore, the distance between points D and C is approximately 32.72 inches.
now how long does Emaniee’s ramp need to be?
To determine the length of Emaniee's ramp, we need to find the distance between points A and C. This will give us the vertical distance that the ramp needs to cover.
Using the Pythagorean theorem, we can calculate the distance between A and C as follows:
hypotenuse^2 = (distance between A and B)^2 + (distance between B and C)^2
Let's substitute the previously calculated values:
hypotenuse^2 = 13.04^2 + 30.82^2
hypotenuse^2 = 170.0816 + 948.7524
hypotenuse^2 = 1118.834
Taking the square root of both sides, we find:
hypotenuse ≈ √1118.834
hypotenuse ≈ 33.45 inches
Therefore, Emaniee's ramp needs to be approximately 33.45 inches long to cover the distance between points A and C.
To compute the distance between points B and C in the given right triangle, you 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 lengths of the other two sides.
In this case, the lengths of the two sides are given as 7 inches and 11 inches, and we need to find the length of the hypotenuse. Let's label the hypotenuse as x.
Using the Pythagorean theorem, we have:
x^2 = 7^2 + 11^2
x^2 = 49 + 121
x^2 = 170
To find the value of x, we need to take the square root of both sides:
x = sqrt(170)
Using a calculator, we find that the square root of 170 is approximately 13.04 inches.
So, the distance between points B and C in the right triangle is approximately 13.04 inches.