Question

What is the length of the hypotenuse? If necessary, round to the nearest tenth. a = 1.4 b = 6.2

Answer 1

To find the length of the hypotenuse in a right triangle when the lengths of the two other sides (legs) are given, you can use the Pythagorean theorem, which is formulated as:

\[ c = \sqrt{a^2 + b^2} \]

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

Given:
- \( a = 1.4 \)
- \( b = 6.2 \)

First, calculate \( a^2 \) and \( b^2 \):

\[
a^2 = (1.4)^2 = 1.96
\]
\[
b^2 = (6.2)^2 = 38.44
\]

Next, add these two values together:

\[
a^2 + b^2 = 1.96 + 38.44 = 40.4
\]

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

\[
c = \sqrt{40.4} \approx 6.36
\]

Finally, round to the nearest tenth:

\[
c \approx 6.4
\]

So, the length of the hypotenuse is approximately **6.4**.