To solve this problem, we can use the Pythagorean Theorem, which 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 other two sides.
In this case, the ladder forms a right triangle with the ground (the base of the house) and the wall (the height Sylvia needs to reach). The ladder is the hypotenuse of the triangle, and the distance from the base of the house to the ladder is one side of the triangle. We can call this distance x, and the height of the ladder is the other side of the triangle.
According to the problem, the distance from the base of the house to the ladder is 6 ft, which we will call x. The length of the ladder (the hypotenuse) is 12 ft.
Using the Pythagorean Theorem, we can write the equation:
x^2 + h^2 = 12^2
Since we are looking for the height of the ladder (h), we can solve for h by substituting x=6 into the equation:
6^2 + h^2 = 12^2
36 + h^2 = 144
Now, we can solve for h by subtracting 36 from both sides and then taking the square root of both sides:
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides gives us:
h = √108
h ≈ 10.4 ft
Therefore, the ladder will reach approximately 10.4 ft high so that Sylvia can replace the siding.
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
10.4 ft.
10.4 ft.
180 ft.
180 ft.
108 ft.
108 ft.
13.4 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.
22.4 ft.
22.4 ft.
300 ft.
300 ft.
500 ft
Responses
17.3 ft.
17.3 ft.
22.4 ft.
22.4 ft.
300 ft.
300 ft.
500 ft
To solve this problem, we can again use the Pythagorean Theorem. In this case, the cable forms a right triangle with the ground and the pole. The cable is the hypotenuse of the triangle, the distance from the base of the pole to the ground is one side of the triangle, and the height of the pole is the other side of the triangle.
According to the problem, the distance from the base of the pole to the ground is 10 ft, which we will call x. The height of the pole (the other side of the triangle) is 20 ft. We are asked to find the length of the cable (the hypotenuse).
Using the Pythagorean Theorem, we can write the equation:
x^2 + 20^2 = cable^2
Since we are looking for the length of the cable, we can solve for cable by substituting x=10 into the equation:
10^2 + 20^2 = cable^2
100 + 400 = cable^2
500 = cable^2
Now, we can solve for cable by taking the square root of both sides:
cable = √500
cable ≈ 22.4 ft
Therefore, the length of the cable is approximately 22.4 ft.
According to the problem, the distance from the base of the pole to the ground is 10 ft, which we will call x. The height of the pole (the other side of the triangle) is 20 ft. We are asked to find the length of the cable (the hypotenuse).
Using the Pythagorean Theorem, we can write the equation:
x^2 + 20^2 = cable^2
Since we are looking for the length of the cable, we can solve for cable by substituting x=10 into the equation:
10^2 + 20^2 = cable^2
100 + 400 = cable^2
500 = cable^2
Now, we can solve for cable by taking the square root of both sides:
cable = √500
cable ≈ 22.4 ft
Therefore, 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.(1 point)
Responses
22.0 ft.
22.0 ft.
7.9 ft.
7.9 ft.
4.7 ft.
4.7 ft.
62.5 ft.
Responses
22.0 ft.
22.0 ft.
7.9 ft.
7.9 ft.
4.7 ft.
4.7 ft.
62.5 ft.
To solve this problem, we can again use the Pythagorean Theorem. In this case, the support bracket forms a right triangle with the ground, the base of the pole, and the point where the bracket is attached on the pole. The bracket itself is the hypotenuse of the triangle, the distance from the base of the pole to the braced point on the pole is one side of the triangle, and the distance from the braced point on the pole to the ground is the other side of the triangle.
According to the problem, the distance from the ground to the braced point on the pole is 4.5 ft, which we will call x. The length of the bracket (the hypotenuse) is 6.5 ft.
Using the Pythagorean Theorem, we can write the equation:
x^2 + 4.5^2 = 6.5^2
Since we are looking for the distance from the base of the pole to the braced point on the pole, we can solve for x.
x^2 + 20.25 = 42.25
x^2 = 42.25 - 20.25
x^2 = 22
Taking the square root of both sides gives us:
x = √22
x ≈ 4.7 ft
Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.
According to the problem, the distance from the ground to the braced point on the pole is 4.5 ft, which we will call x. The length of the bracket (the hypotenuse) is 6.5 ft.
Using the Pythagorean Theorem, we can write the equation:
x^2 + 4.5^2 = 6.5^2
Since we are looking for the distance from the base of the pole to the braced point on the pole, we can solve for x.
x^2 + 20.25 = 42.25
x^2 = 42.25 - 20.25
x^2 = 22
Taking the square root of both sides gives us:
x = √22
x ≈ 4.7 ft
Therefore, each bracket should be braced in the ground approximately 4.7 ft from the base of the pole.
1 answer