Finding the missing side of the right triangle. Round your answer to the nearest tenth. One side of the triangle labeled as 27 and the other is 11

Answer 1

To find the missing side of a right triangle with one side measuring 27 and the other side measuring 11, we can use the Pythagorean theorem, which states:

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

where \( c \) is the length of the hypotenuse (the longest side) and \( a \) and \( b \) are the lengths of the other two sides.

Assuming that 27 is the hypotenuse (c) and 11 is one of the sides (a), we can find the missing side (b) using:

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

Substituting the known values:

\[ 27^2 = 11^2 + b^2 \]

Calculating the squares:

\[ 729 = 121 + b^2 \]

Now, subtract 121 from both sides:

\[ 729 - 121 = b^2 \]

\[ 608 = b^2 \]

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

\[ b = \sqrt{608} \approx 24.6 \]

So the missing side, rounded to the nearest tenth, is approximately 24.6.

If instead you meant for 27 to be one of the shorter sides (not the hypotenuse), please let me know!

Answer 2

Use the Pythagorean Theorem

Answer 3

Certainly! Let’s use the Pythagorean Theorem more explicitly to find the missing side of the right triangle.

The Pythagorean theorem states:

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

where \( c \) is the hypotenuse, and \( a \) and \( b \) are the two other sides of the triangle.

Case 1: 27 is the hypotenuse

If we assume that 27 is the hypotenuse and 11 is one of the legs (let's say \( a = 11 \)), we can find the missing side \( b \):

1. Substitute into the theorem:

\[ 11^2 + b^2 = 27^2 \]

2. Calculate \( 11^2 \) and \( 27^2 \):

\[ 121 + b^2 = 729 \]

3. Solve for \( b^2 \):

\[ b^2 = 729 - 121 \] \[ b^2 = 608 \]

4. Take the square root to find \( b \):

\[ b = \sqrt{608} \approx 24.6 \]

Case 2: 27 is one of the legs

If we assume that \( a = 27 \) and \( b = 11 \), we can find the hypotenuse \( c \):

1. Substitute into the theorem:

\[ 27^2 + 11^2 = c^2 \]

2. Calculate \( 27^2 \) and \( 11^2 \):

\[ 729 + 121 = c^2 \]

3. Solve for \( c^2 \):

\[ c^2 = 729 + 121 \] \[ c^2 = 850 \]

4. Take the square root to find \( c \):

\[ c = \sqrt{850} \approx 29.2 \]

Summary of Results:

• If 27 is the hypotenuse, the missing side is approximately 24.6.
• If 27 is one of the legs, the hypotenuse is approximately 29.2.

Let me know if you need further assistance!

Answer 4

Find the base of the triangle. The perpendicular side is labeled as 11 and the hypotenuse is 27. Hopefully this helps you solve the problem

Answer 5

Thank you for the clarification! Given that the hypotenuse is 27 and one of the perpendicular sides (the leg) is 11, we can use the Pythagorean theorem to find the length of the base (the other perpendicular side).

Using the Pythagorean theorem:

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

where:

• \( c \) is the hypotenuse (27),
• \( a \) is one leg (11),
• \( b \) is the other leg (the base we want to find).

Substituting the known values into the equation:

\[ 11^2 + b^2 = 27^2 \]

Calculating the squares:

\[ 121 + b^2 = 729 \]

Now, isolate \( b^2 \):

\[ b^2 = 729 - 121 \] \[ b^2 = 608 \]

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

\[ b = \sqrt{608} \approx 24.6 \]

Thus, the base of the triangle is approximately 24.6, rounded to the nearest tenth.

Answer 6

Still wrong

Answer 7

I apologize for any confusion. Let's carefully go through the calculation again.

Given:

• The perpendicular side (one leg) \( a = 11 \)
• The hypotenuse \( c = 27 \)

We want to find the base of the triangle, which we can denote as \( b \).

Using the Pythagorean Theorem:

The relationship is given by the formula:

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

Substituting the known values into the equation:

\[ 11^2 + b^2 = 27^2 \]

Calculating the squares:

\[ 121 + b^2 = 729 \]

Now, isolate \( b^2 \):

\[ b^2 = 729 - 121 \] \[ b^2 = 608 \]

Taking the square root of both sides:

\[ b = \sqrt{608} \]

Simplifying \(\sqrt{608}\):

To simplify:

\[ 608 = 16 \times 38 \]

Thus,

\[ b = \sqrt{16 \times 38} = \sqrt{16} \times \sqrt{38} = 4\sqrt{38} \]

Calculating \( \sqrt{38} \approx 6.1644 \), so:

\[ b \approx 4 \times 6.1644 \approx 24.658 \]

Rounded to the nearest tenth:

\[ b \approx 24.7 \]

So, the base of the triangle is approximately 24.7.

If this isn't what you were looking for or if you meant something else, please let me know, and we'll get it sorted out!