What is the length of the hypotenuse? If necessary, round to the nearest tenth. a=7 b=2.3

To find the length of the hypotenuse in a right triangle, you can use the Pythagorean theorem:

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

Given that \( a = 7 \) and \( b = 2.3 \), we want to find the hypotenuse \( c \).

1. Substitute the known values into the equation:

\[
c^2 = 7^2 + 2.3^2
\]

2. Calculate \( 7^2 \) and \( 2.3^2 \):

\[
7^2 = 49
\]
\[
2.3^2 = 5.29
\]

3. Add these values:

\[
c^2 = 49 + 5.29 = 54.29
\]

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

\[
c = \sqrt{54.29} \approx 7.37
\]

Rounding to the nearest tenth:

\[
c \approx 7.4
\]

So, the length of the hypotenuse \( c \) is approximately **7.4**.

Would you like more details or have any questions?

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Here are 8 related questions:
1. How do you solve for one of the legs when given the hypotenuse and the other leg?
2. What are the typical applications of the Pythagorean theorem in real-life scenarios?
3. How do you use the Pythagorean theorem in three-dimensional geometry?
4. Can the Pythagorean theorem be used to solve problems in non-Euclidean geometry?
5. What are some examples of numbers that form Pythagorean triples?
6. How does the length of the hypotenuse relate to the angles in a right triangle?
7. How do you calculate the area of a right triangle using the lengths of the legs?
8. How does the Pythagorean theorem help in determining distances in coordinate geometry?

**Tip:** When solving for the hypotenuse, ensure that you carefully square each side and correctly sum them before taking the square root.

Discover how to find the length of the hypotenuse in a right triangle with sides a=7 and b=2.3 using the Pythagorean theorem. Step-by-step solution included, rounding to the nearest tenth.

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