Triangle GHI is a right triangle. The length of one leg is 11 and the hypotenuse is 22. What is the length of the other leg? Round your answer to two decimal places. I tried 19.08 and 19.07, still wrong. One try left.

Answer 1

To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which states that:

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

where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the triangle. In this case, we know one leg (\(a\)) is 11, and the hypotenuse (\(c\)) is 22. We need to find the length of the other leg (\(b\)).

Substituting the known values into the equation:

\[ 11^2 + b^2 = 22^2 \]

Calculating the squares:

\[ 121 + b^2 = 484 \]

Next, we isolate \(b^2\):

\[ b^2 = 484 - 121 \] \[ b^2 = 363 \]

Now we take the square root of both sides to find \(b\):

\[ b = \sqrt{363} \]

Calculating the square root:

\[ b \approx 19.08 \]

However, since you've already tried this answer and didn't get it correct, let’s round it to two decimal places:

Calculating \( \sqrt{363} \) more precisely:

\[ b \approx 19.052558 \]

So when rounded to two decimal places:

\[ b \approx 19.05 \]

Thus, the length of the other leg is approximately 19.05.

Answer 2

Correct. Thank you!

Answer 3

You're welcome! I'm glad to hear that the answer was correct. If you have any more questions or need further assistance, feel free to ask. Happy studying!

Answer 4

If the equation 18 (squared) 2 + b (squared) 2 = 30 (squared) 2 is found to be true, what do we know about the triangle?
The triangle is a right triangle, and the hypotenuse is 18.
The triangle is a right triangle with a missing leg length of 24.
The triangle is a right triangle, and the legs are 30 and 24.
The triangle is a right triangle with a missing side of 34.99.

Answer 5

To analyze the given equation \(18^2 + b^2 = 30^2\), we can determine the properties of the triangle based on the values involved.

1. Calculate \(18^2\) and \(30^2\):

   • \(18^2 = 324\)
   • \(30^2 = 900\)

2. Substitute these values into the equation: \[ 324 + b^2 = 900 \]

3. Now, isolate \(b^2\): \[ b^2 = 900 - 324 \] \[ b^2 = 576 \]

4. Take the square root to find \(b\): \[ b = \sqrt{576} = 24 \]

Now, let's analyze the answers given in your question:

• The triangle is a right triangle, and the hypotenuse is 18. (Incorrect: the hypotenuse is 30.)
• The triangle is a right triangle with a missing leg length of 24. (Correct: we found \(b = 24\).)
• The triangle is a right triangle, and the legs are 30 and 24. (Incorrect: 30 is the hypotenuse, not a leg.)
• The triangle is a right triangle with a missing side of 34.99. (Incorrect: we found the missing leg, which is 24.)

The correct statement is: The triangle is a right triangle with a missing leg length of 24.

Answer 6

A triangle is drawn and squares are created from the lengths of each side. Square A has an area of 18 units (squared) 2 and Square B has an area of 90 units (squared) 2. What must be the area of the 3rd square for triangle to have a right angle?

Answer 7

To determine the area of the third square such that the triangle can have a right angle, we can use the Pythagorean theorem. This theorem states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\):

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

From the given information:

• Square A has an area of 18 units², so we can let \(a^2 = 18\).
• Square B has an area of 90 units², so we can let \(b^2 = 90\).

The area of the third square, which represents the hypotenuse \(c^2\), is what we need to find:

Using the Pythagorean theorem: \[ 18 + 90 = c^2 \] \[ c^2 = 108 \]

Thus, the area of the third square must be \(108\) square units.