Using the Pythagorean theorem, we can find the length of the hypotenuse.
The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of the two legs (a and b).
In this case, the legs are both 12 cm long. So, a = b = 12 cm.
Using the formula, we have:
c^2 = a^2 + b^2
c^2 = 12^2 + 12^2
c^2 = 144 + 144
c^2 = 288
Taking the square root of both sides, we have:
c = √288
c ≈ 16.97 (rounded to the nearest hundredth)
Therefore, the length of the hypotenuse is approximately 16.97 cm, which corresponds to the first answer choice.
So, the correct answer is:
• 16.97
If a right triangle has legs that are both 12 cm long, how long is the hypotenuse? Round the answer to the nearest hundredth.
• 16.97
• Not enough information is given to solve the problem.
© 288
• 17.0
7 answers
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)
To solve this problem, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square 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 base of the house and the ground.
Let's label the height the ladder will reach as "h" and the base of the ladder as 6 ft.
We can set up the equation using the Pythagorean theorem:
h^2 = 12^2 - 6^2
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we have:
h = √108 ≈ 10.39 (rounded to the nearest tenth)
Therefore, the ladder will reach a height of approximately 10.39 ft, which corresponds to the second answer choice.
So, the correct answer is:
• 10.4
The Pythagorean theorem states that in a right triangle, the square 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 base of the house and the ground.
Let's label the height the ladder will reach as "h" and the base of the ladder as 6 ft.
We can set up the equation using the Pythagorean theorem:
h^2 = 12^2 - 6^2
h^2 = 144 - 36
h^2 = 108
Taking the square root of both sides, we have:
h = √108 ≈ 10.39 (rounded to the nearest tenth)
Therefore, the ladder will reach a height of approximately 10.39 ft, which corresponds to the second answer choice.
So, the correct answer is:
• 10.4
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)
To solve this problem, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square 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 cable forms a right triangle with the base of the pole and the ground.
Let's label the length of the cable as "c", the height of the pole as 20 ft, and the distance from the base of the pole to the anchor point as 10 ft.
We can set up the equation using the Pythagorean theorem:
c^2 = 20^2 + 10^2
c^2 = 400 + 100
c^2 = 500
Taking the square root of both sides, we have:
c = √500 ≈ 22.36 (rounded to the nearest tenth)
Therefore, the length of the cable is approximately 22.36 ft, which corresponds to the third answer choice.
So, the correct answer is:
• 22.4
The Pythagorean theorem states that in a right triangle, the square 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 cable forms a right triangle with the base of the pole and the ground.
Let's label the length of the cable as "c", the height of the pole as 20 ft, and the distance from the base of the pole to the anchor point as 10 ft.
We can set up the equation using the Pythagorean theorem:
c^2 = 20^2 + 10^2
c^2 = 400 + 100
c^2 = 500
Taking the square root of both sides, we have:
c = √500 ≈ 22.36 (rounded to the nearest tenth)
Therefore, the length of the cable is approximately 22.36 ft, which corresponds to the third answer choice.
So, the correct answer is:
• 22.4
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)
Round to the nearest tenth. (1 point)
To solve this problem, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square 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, we can consider a right triangle formed by the base of the pole, the braced point in the ground, and the point on the pole where the bracket is attached.
Let's label the distance from the base of the pole to the braced point in the ground as "x" ft and the length of the bracket as 6.5 ft.
We know that the point on the pole where the bracket is attached is 4.5 ft from the ground.
We can set up the equation using the Pythagorean theorem:
x^2 = 6.5^2 - 4.5^2
x^2 = 42.25 - 20.25
x^2 = 22
Taking the square root of both sides, we have:
x = √22 ≈ 4.69 (rounded to the nearest tenth)
Therefore, each bracket should be braced in the ground approximately 4.69 ft from the base of the pole, which corresponds to the fourth answer choice.
So, the correct answer is:
• 4.7
The Pythagorean theorem states that in a right triangle, the square 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, we can consider a right triangle formed by the base of the pole, the braced point in the ground, and the point on the pole where the bracket is attached.
Let's label the distance from the base of the pole to the braced point in the ground as "x" ft and the length of the bracket as 6.5 ft.
We know that the point on the pole where the bracket is attached is 4.5 ft from the ground.
We can set up the equation using the Pythagorean theorem:
x^2 = 6.5^2 - 4.5^2
x^2 = 42.25 - 20.25
x^2 = 22
Taking the square root of both sides, we have:
x = √22 ≈ 4.69 (rounded to the nearest tenth)
Therefore, each bracket should be braced in the ground approximately 4.69 ft from the base of the pole, which corresponds to the fourth answer choice.
So, the correct answer is:
• 4.7