Question

what is the length of the hypotenuse if necessary round to the nearest tenth 2.6 ft and 8.3 ft

Answer 1

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

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

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

In this case, \( a = 2.6 \, \text{ft} \) and \( b = 8.3 \, \text{ft} \).

First, square both lengths:

\[
2.6^2 = 6.76
\]
\[
8.3^2 = 68.89
\]

Now, add the squares of the two sides:

\[
6.76 + 68.89 = 75.65
\]

Next, take the square root to find the length of the hypotenuse:

\[
c = \sqrt{75.65} \approx 8.694
\]

Rounding to the nearest tenth:

\[
c \approx 8.7 \, \text{ft}
\]

Therefore, the length of the hypotenuse is approximately **8.7 ft**.