Let h be the height of the ladder. Using the Pythagorean theorem, we can write the equation (6)^2 + h^2 = (12)^2.
Expanding the equation, we get 36 + h^2 = 144.
Subtracting 36 from both sides, we get h^2 = 108.
Taking the square root of both sides, we get h = ±√108.
Since the ladder cannot have a negative height, we take the positive value.
Therefore, h = √108 ≈ 10.4.
So, the ladder will reach a height of approximately 10.4 ft. Answer: \boxed{10.4}.
Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding?
10 answers
An electric pole has a support cable that is attached to the pole 20 ft. from the ground. The cable is anchored on the ground 10 ft. from the base of the pole. How long is the cable? Round to the nearest tenth.
To find the length of the cable, we can use the Pythagorean Theorem.
Let 'c' be the length of the cable.
According to the given information, the height of the pole is 20 ft and the distance from the base of the pole to the anchor point on the ground is 10 ft. These two dimensions form a right-angled triangle, with the cable acting as the hypotenuse.
Using the Pythagorean theorem, we can write the equation:
c^2 = (length of one side)^2 + (length of the other side)^2
In this case, the two sides are the height of the pole and the distance from the base of the pole to the anchor point on the ground.
Substituting the given values, we have:
c^2 = 20^2 + 10^2
Simplifying the equation, we have:
c^2 = 400 + 100
c^2 = 500
To find the value of 'c', we need to take the square root of both sides of the equation:
c ≈ sqrt(500)
Using a calculator, the square root of 500 is approximately 22.4 ft.
Therefore, rounding to the nearest tenth, the length of the cable is approximately 22.4 ft.
Let 'c' be the length of the cable.
According to the given information, the height of the pole is 20 ft and the distance from the base of the pole to the anchor point on the ground is 10 ft. These two dimensions form a right-angled triangle, with the cable acting as the hypotenuse.
Using the Pythagorean theorem, we can write the equation:
c^2 = (length of one side)^2 + (length of the other side)^2
In this case, the two sides are the height of the pole and the distance from the base of the pole to the anchor point on the ground.
Substituting the given values, we have:
c^2 = 20^2 + 10^2
Simplifying the equation, we have:
c^2 = 400 + 100
c^2 = 500
To find the value of 'c', we need to take the square root of both sides of the equation:
c ≈ sqrt(500)
Using a calculator, the square root of 500 is approximately 22.4 ft.
Therefore, rounding to the nearest tenth, the length of the cable is approximately 22.4 ft.
A streetlight post needs some extra support for potential bad weather and high winds. The city wants to install metal support brackets on the light post. Each bracket will be braced into the ground and will then attach to a point on the pole that is 4.5 ft. from the ground. Each bracket is 6.5 ft. long. How far from the base of the pole should each bracket be braced in the ground? Round to the nearest tenth.
To find the distance from the base of the pole where each bracket should be braced into the ground, we can use the Pythagorean Theorem.
Let 'd' be the distance from the base of the pole where each bracket should be braced into the ground.
According to the given information, each bracket is 6.5 ft long and attached to a point on the pole that is 4.5 ft from the ground. These two dimensions form a right-angled triangle, with the distance from the base of the pole to where each bracket is braced into the ground acting as one side.
Using the Pythagorean theorem, we can write the equation:
d^2 = (length of one side)^2 + (length of the other side)^2
In this case, the two sides are the length of each bracket and the distance from the point on the pole to the ground.
Substituting the given values, we have:
d^2 = 6.5^2 + 4.5^2
Simplifying the equation, we have:
d^2 = 42.25 + 20.25
d^2 = 62.5
To find the value of 'd', we need to take the square root of both sides of the equation:
d ≈ sqrt(62.5)
Using a calculator, the square root of 62.5 is approximately 7.9 ft.
Therefore, rounding to the nearest tenth, each bracket should be braced in the ground approximately 7.9 ft from the base of the pole.
Let 'd' be the distance from the base of the pole where each bracket should be braced into the ground.
According to the given information, each bracket is 6.5 ft long and attached to a point on the pole that is 4.5 ft from the ground. These two dimensions form a right-angled triangle, with the distance from the base of the pole to where each bracket is braced into the ground acting as one side.
Using the Pythagorean theorem, we can write the equation:
d^2 = (length of one side)^2 + (length of the other side)^2
In this case, the two sides are the length of each bracket and the distance from the point on the pole to the ground.
Substituting the given values, we have:
d^2 = 6.5^2 + 4.5^2
Simplifying the equation, we have:
d^2 = 42.25 + 20.25
d^2 = 62.5
To find the value of 'd', we need to take the square root of both sides of the equation:
d ≈ sqrt(62.5)
Using a calculator, the square root of 62.5 is approximately 7.9 ft.
Therefore, rounding to the nearest tenth, each bracket should be braced in the ground approximately 7.9 ft from the base of the pole.
wrong bot the answer is supposed to be 4.7
Use the Pythagorean theorem quick check answers
1. 14.7
2. 16.97
3. 10.4
4. 22.4
5. 4.7
(NOTE: the answers are only correct if you have the same questions as her. follow my page and I give out more answers for 8th grade quick checks and unit test!!
1. 14.7
2. 16.97
3. 10.4
4. 22.4
5. 4.7
(NOTE: the answers are only correct if you have the same questions as her. follow my page and I give out more answers for 8th grade quick checks and unit test!!
ily sm pookie
bro what's up with ur user @c*mshots.
kids these days