To solve this problem, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. In this case, the ladder forms a right triangle with the base of the house and the ground.
We know that the base of the ladder is 6 ft and the length of the ladder is 12 ft. Let's represent the height of the ladder as 'h'. Using the Pythagorean Theorem, we can set up the equation:
(6^2) + (h^2) = (12^2)
36 + h^2 = 144
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we find:
h = √(108)
h ≈ 10.4 ft
Therefore, the ladder will reach approximately 10.4 ft high so that Sylvia can replace the siding on her house.
The correct answer is:
10.4 ft.
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?(1 point)
Responses
180 ft.
180 ft.
10.4 ft.
10.4 ft.
13.4 ft.
13.4 ft.
108 ft.
5 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.(1 point)
Responses
17.3 ft.
17.3 ft.
500 ft.
500 ft.
22.4 ft.
22.4 ft.
300 ft.
Responses
17.3 ft.
17.3 ft.
500 ft.
500 ft.
22.4 ft.
22.4 ft.
300 ft.
To solve this problem, we can again use the Pythagorean Theorem.
Let the length of the cable be 'c'. We know that the height of the pole is 20 ft and the distance between the pole and the anchoring point on the ground is 10 ft.
Using the Pythagorean Theorem, we can set up the equation:
(10^2) + (20^2) = c^2
100 + 400 = c^2
500 = c^2
Taking the square root of both sides, we find:
c ≈ √500
c ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
The correct answer is:
22.4 ft.
Let the length of the cable be 'c'. We know that the height of the pole is 20 ft and the distance between the pole and the anchoring point on the ground is 10 ft.
Using the Pythagorean Theorem, we can set up the equation:
(10^2) + (20^2) = c^2
100 + 400 = c^2
500 = c^2
Taking the square root of both sides, we find:
c ≈ √500
c ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
The correct answer is:
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.(1 point)
Responses
62.5 ft.
62.5 ft.
7.9 ft.
7.9 ft.
22.0 ft.
22.0 ft.
4.7 ft.
Responses
62.5 ft.
62.5 ft.
7.9 ft.
7.9 ft.
22.0 ft.
22.0 ft.
4.7 ft.
To solve this problem, we can use the Pythagorean Theorem once again.
Let the distance from the base of the pole to the bracing point in the ground be 'd'. We know that the height of the bracing point on the pole is 4.5 ft and the length of the bracket is 6.5 ft.
Using the Pythagorean Theorem, we can set up the equation:
(d^2) + (4.5^2) = (6.5^2)
d^2 + 20.25 = 42.25
d^2 = 42.25 - 20.25
d^2 = 22
Taking the square root of both sides, we find:
d ≈ √22
d ≈ 4.7 ft
Therefore, each bracket should be braced approximately 4.7 ft from the base of the pole in the ground.
The correct answer is:
4.7 ft.
Let the distance from the base of the pole to the bracing point in the ground be 'd'. We know that the height of the bracing point on the pole is 4.5 ft and the length of the bracket is 6.5 ft.
Using the Pythagorean Theorem, we can set up the equation:
(d^2) + (4.5^2) = (6.5^2)
d^2 + 20.25 = 42.25
d^2 = 42.25 - 20.25
d^2 = 22
Taking the square root of both sides, we find:
d ≈ √22
d ≈ 4.7 ft
Therefore, each bracket should be braced approximately 4.7 ft from the base of the pole in the ground.
The correct answer is:
4.7 ft.