Question

find the length of the missing side for this right triangle. Estimate an irrational answer to two decimal places

right side=8
hypotenuse= 13
bottom=?

Answer 1

To find the length of the missing side (the bottom side) of a right triangle, we can use the Pythagorean theorem, which states:

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

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

In your case:
- The right side (one leg) is \(8\).
- The hypotenuse (\(c\)) is \(13\).
- Let \(b\) be the length of the bottom side (the other leg).

According to the Pythagorean theorem, we can write:

\[
8^2 + b^2 = 13^2
\]

Calculating the squares:

\[
64 + b^2 = 169
\]

Now, subtract \(64\) from both sides:

\[
b^2 = 169 - 64
\]
\[
b^2 = 105
\]

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

\[
b = \sqrt{105}
\]

To estimate \(b\) to two decimal places, we calculate:

\[
\sqrt{105} \approx 10.247
\]

Rounding to two decimal places:

\[
b \approx 10.25
\]

Therefore, the length of the bottom side is approximately **10.25**.