Rosanna calculates that the length of is 225 in. What needs to be corrected in her calculation?

Question

(1 point)
c𝑐
Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both s
Rosanna’s answer is right because she correctly applied the Pythagorean Theorem.
Rosanna should take the square root of the sum when using the Pythagorean Theorem.
Rosanna forgot to divide the answer she found through the Pythagorean Theorem by 2.

Answer 1

To determine what needs to be corrected in Rosanna's calculation, we can consider the context of how she arrived at the length of 225 in. If she is working with a right triangle and applying the Pythagorean Theorem, the correct formula is:

\[ c^2 = a^2 + b^2 \]

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs.

1. If Rosanna mistakenly added the squared hypotenuse with the square of the longest leg instead of adding both legs, her calculation would be incorrect.
2. If she applied the Pythagorean Theorem correctly, then her answer would be right.
3. If she arrived at the length of 225 inches by summing the squares of the legs without taking the square root, then she did not follow the Pythagorean Theorem correctly, which requires taking the square root of the sum.
4. The idea of dividing the answer by 2 does not apply in the context of the Pythagorean Theorem.

Based on these considerations, the most appropriate correction would be:

Rosanna should take the square root of the sum when using the Pythagorean Theorem.

This option correctly identifies a common error in using the theorem.

Answer 2

If triangle ABC 𝐴𝐵𝐶 has sides measuring 39, 15, and 36, is the triangle a right triangle?(1 point)
No, because 39
2 + 15
2 ≠ 36
2 39 + ≠
2 15
2 36
2
Yes, because 1,521 equals 1,521.
No, because the sum of the squared legs do not equal the square root of the hypotenuse.
Yes, because 1,746 equals 1,746.

Answer 3

To determine if triangle ABC with sides measuring 39, 15, and 36 is a right triangle, we can apply the Pythagorean Theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the sides are:

• \( a = 15 \)
• \( b = 36 \)
• \( c = 39 \) (the longest side)

We will check if the following condition holds:

\[ c^2 = a^2 + b^2 \]

Calculating the squares:

1. \( c^2 = 39^2 = 1521 \)
2. \( a^2 = 15^2 = 225 \)
3. \( b^2 = 36^2 = 1296 \)

Now, we add \( a^2 \) and \( b^2 \):

\[ a^2 + b^2 = 225 + 1296 = 1521 \]

Since \( c^2 = a^2 + b^2 \):

\[ 1521 = 1521 \]

This confirms that the triangle is indeed a right triangle.

So the correct answer is:

Yes, because 1,521 equals 1,521.

Answer 4

Can a triangle with sides 7, 10, and 12 be a right triangle? How do you know?(1 point)
No, because 149 does not equal 144.
Yes, because it looks like a right triangle.
No, because 193 does not equal 100.
There is no way to tell without an angle measure

Answer 5

To determine if a triangle with sides measuring 7, 10, and 12 can be a right triangle, we will again use the Pythagorean Theorem. According to the theorem, a triangle is a right triangle if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides.

1. Identify the lengths of the sides: \( a = 7 \), \( b = 10 \), and \( c = 12 \) (the longest side).
2. Check if \( c^2 = a^2 + b^2 \).

Calculating the squares:

• \( c^2 = 12^2 = 144 \)
• \( a^2 = 7^2 = 49 \)
• \( b^2 = 10^2 = 100 \)

Now, we add \( a^2 \) and \( b^2 \):

\[ a^2 + b^2 = 49 + 100 = 149 \]

Now we check if \( c^2 = a^2 + b^2 \):

\[ 144 \neq 149 \]

Since \( 144 \) does not equal \( 149 \), this indicates that a triangle with sides 7, 10, and 12 cannot be a right triangle.

The correct answer is:

No, because 149 does not equal 144.

Answer 6

An outdoor movie screen is 30 ft. tall. It needs additional support to keep it upright and prevent it from
leaning. The town has decided to attach 15 ft. metal brackets to the back of the screen. The best spot
to anchor the brackets to the ground is 6 ft. from the base of the screen. How far from the ground
should the brackets be attached to the frame of the screen to ensure that the screen is at a right angle
with the ground? Round to the nearest hundredth.
(1 point)
15 ft.
29.39 ft.
13.75 ft.
16.16 ft.

Answer 7

To find out how far from the ground the brackets should be attached to the frame of the screen in order to ensure that it forms a right triangle with the ground and the support brackets, we can use the Pythagorean theorem.

In this scenario, we have:

• One leg of the triangle (the distance from the base to the ground) = 6 ft (the horizontal distance from the base of the screen to the ground anchor).
• The other leg of the triangle (the length of the metal bracket) = 15 ft (the length of the brackets).

Let \( h \) be the height at which the brackets are attached to the screen (the vertical leg of the triangle). According to the Pythagorean theorem:

\[ a^2 + b^2 = c^2 \]

Where:

• \( a \) is the horizontal distance (6 ft),
• \( b \) is the height at which the bracket will be attached (which we need to find),
• \( c \) is the length of the bracket (15 ft).

So we have:

\[ 6^2 + h^2 = 15^2 \]

Calculating the squares:

\[ 36 + h^2 = 225 \]

Now, we will solve for \( h^2 \):

\[ h^2 = 225 - 36 \] \[ h^2 = 189 \]

Next, take the square root to find \( h \):

\[ h = \sqrt{189} \approx 13.75 , \text{ft} \]

Thus, the height at which the brackets should be attached to the frame of the screen is approximately 13.75 ft.

The correct answer is:

13.75 ft.

Answer 8

A volleyball net post needs a cable to support it. The hook to attach the cable is 4 ft. above the court
surface, and the hook in the floor is 3 ft. from the base of the post. How long should the cable be?
(1 point)
25 ft.
4 ft.
5 ft.
2.65 ft.

Answer 9

To find the length of the cable needed to support the volleyball net post, we can visualize the situation as a right triangle where:

• One leg of the triangle is the vertical height from the hook above the court surface to the floor (4 ft).
• The other leg of the triangle is the horizontal distance from the base of the post to the point on the floor where the hook is attached (3 ft).
• The hypotenuse will be the length of the cable.

We can use the Pythagorean theorem to find the length of the cable:

\[ c^2 = a^2 + b^2 \]

Where:

• \( c \) is the length of the cable (hypotenuse),
• \( a \) is the vertical height (4 ft),
• \( b \) is the horizontal distance (3 ft).

Substituting the values into the equation:

\[ c^2 = 4^2 + 3^2 \] \[ c^2 = 16 + 9 \] \[ c^2 = 25 \]

Now, take the square root to find \( c \):

\[ c = \sqrt{25} = 5 , \text{ft} \]

Thus, the length of the cable should be 5 ft.

The correct answer is:

5 ft.