Question

What is the length of the hypotenuse? If necessary, round to the nearest tenth. a = 1.1 b = 0.8

Answer 1

To find the length of the hypotenuse in a right triangle, we 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.

Given \(a = 1.1\) and \(b = 0.8\), we can plug in these values:

\[
c = \sqrt{(1.1)^2 + (0.8)^2}
\]

Calculating \(1.1^2\) and \(0.8^2\):

\[
1.1^2 = 1.21
\]
\[
0.8^2 = 0.64
\]

Now adding these values:

\[
c = \sqrt{1.21 + 0.64} = \sqrt{1.85}
\]

Now, let's calculate \(\sqrt{1.85}\):

\[
\sqrt{1.85} \approx 1.36
\]

Rounding to the nearest tenth:

\[
c \approx 1.4
\]

Therefore, the length of the hypotenuse is approximately **1.4**.