A right triangle has leg lengths of 5 inches and 12 inches. What is the length of the hypotenuse?

Answer 1

To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states:

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

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

In this case, the lengths of the legs are 5 inches and 12 inches. We can plug these values into the equation:

\[ c^2 = 5^2 + 12^2 \]

Calculating \(5^2\) and \(12^2\):

\[ c^2 = 25 + 144 \] \[ c^2 = 169 \]

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

\[ c = \sqrt{169} = 13 \]

Thus, the length of the hypotenuse is \(\boxed{13}\) inches.

Answer 2

The side length of a square tile is 8 inches. Which measurement is closest to the length of a diagonal of this tile in inches?

Answer 3

To find the length of the diagonal of a square tile, we can use the formula for the diagonal \(d\) of a square, which is given by:

\[ d = s\sqrt{2} \]

where \(s\) is the length of one side of the square.

In this case, the side length of the tile is \(s = 8\) inches. Substituting this into the formula gives:

\[ d = 8\sqrt{2} \]

To get a numerical approximation, we can calculate \(\sqrt{2}\):

\[ \sqrt{2} \approx 1.414 \]

Now, substituting this value back into the equation for \(d\):

\[ d \approx 8 \times 1.414 \approx 11.312 \]

Therefore, the length of the diagonal of the tile is closest to approximately \(11.31\) inches. Thus, the measurement closest to the length of the diagonal is \(\approx 11.31\) inches.

Rounding this gives us:

The length of the diagonal is closest to \(\boxed{11.31}\) inches.

Answer 4

The width of a rectangle is 7.9 inches, and the diagonal length of the rectangle is 8.9 inches. Which measurement is closest to the length of this rectangle in inches?

Answer 5

To find the length of the rectangle when given the width and diagonal, we can use the Pythagorean theorem. In a rectangle, the diagonal \(d\) can be expressed as:

\[ d^2 = l^2 + w^2 \]

where \(l\) is the length and \(w\) is the width.

Given:

• Width \(w = 7.9\) inches
• Diagonal \(d = 8.9\) inches

We can plug these values into the equation:

\[ (8.9)^2 = l^2 + (7.9)^2 \]

Calculating the squares:

\[ 8.9^2 = 79.21 \] \[ 7.9^2 = 62.41 \]

Now substituting these values into the equation:

\[ 79.21 = l^2 + 62.41 \]

Next, we can solve for \(l^2\):

\[ l^2 = 79.21 - 62.41 \] \[ l^2 = 16.80 \]

Taking the square root to find \(l\):

\[ l = \sqrt{16.80} \approx 4.1 \]

Thus, the length of the rectangle is approximately \(4.1\) inches. Rounding this gives us:

The measurement closest to the length of the rectangle is \(\boxed{4.1}\) inches.

Answer 6

A right triangle has a leg length of 6 centimeters and a hypotenuse length of 10 centimeters. What is the length of the other leg?

Answer 7

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

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

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs. In this case, we know one leg (\(a = 6\) cm) and the hypotenuse (\(c = 10\) cm), and we need to find the length of the other leg (\(b\)).

Substituting into the equation gives:

\[ 10^2 = 6^2 + b^2 \]

Calculating the squares:

\[ 100 = 36 + b^2 \]

Now, we can solve for \(b^2\):

\[ b^2 = 100 - 36 \] \[ b^2 = 64 \]

Taking the square root of both sides to find \(b\):

\[ b = \sqrt{64} = 8 \]

Therefore, the length of the other leg is \( \boxed{8} \) centimeters.

Answer 8

A right triangle and two of its side lengths are shown in the diagram. Which measurement is closest to the value of x in feet?

Answer 9

It seems you mentioned a diagram related to a right triangle, but unfortunately, I cannot see diagrams or images. However, I can help you solve for \(x\) in a right triangle if you provide the lengths of the other two sides or any relevant information.

If you can provide the lengths of the two sides of the triangle, I can assist you with applying the Pythagorean theorem, or if you need to find an angle using trigonometric ratios, I can provide guidance on that as well.

Please provide any known side lengths or additional information, and I'll be happy to help!

Answer 10

3.7 feet on the left and 14.3 ft at the top

Answer 11

Given that you have a right triangle with side lengths of 3.7 feet and 14.3 feet, we can use the Pythagorean theorem to find the length of the hypotenuse \(x\).

The Pythagorean theorem states:

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

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the two legs of the right triangle. In this case, we can consider:

• \(a = 3.7\) feet
• \(b = 14.3\) feet

Now, we can substitute these values into the equation:

\[ x^2 = (3.7)^2 + (14.3)^2 \]

Calculating \(3.7^2\) and \(14.3^2\):

\[ 3.7^2 = 13.69 \] \[ 14.3^2 = 204.49 \]

Now, substitute these results back into the equation:

\[ x^2 = 13.69 + 204.49 \] \[ x^2 = 218.18 \]

Next, take the square root of both sides to find \(x\):

\[ x = \sqrt{218.18} \approx 14.8 \]

Thus, the measurement closest to the value of \(x\) (the hypotenuse) is approximately \(\boxed{14.8}\) feet.