Question

Finding the missing side of the right triangle. Round your answer to the nearest tenth
the bouttom is 14 and the side is 10

Answer 1

To find the missing side of a right triangle when you have the lengths of two sides, you can use the Pythagorean theorem, which states:

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

where \(c\) is the hypotenuse (the longest side), and \(a\) and \(b\) are the other two sides.

If we assume the bottom side (14) is one leg and the side (10) is the other leg, the equation can be written as:

\[
10^2 + 14^2 = c^2
\]

Calculating this:

\[
100 + 196 = c^2
\]
\[
296 = c^2
\]

Now find \(c\) by taking the square root of both sides:

\[
c = \sqrt{296} \approx 17.2
\]

So, if 14 is one leg and 10 is the other leg, the hypotenuse is approximately **17.2**.

If instead, the 14 is the hypotenuse and you are looking for one of the legs, then the formula rearranges to:

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

Thus, you would have:

\[
14^2 = 10^2 + a^2
\]
\[
196 = 100 + a^2
\]
\[
a^2 = 196 - 100 = 96
\]
\[
a = \sqrt{96} \approx 9.8
\]

So, if 14 is the hypotenuse and 10 is one leg, the missing leg measures approximately **9.8**.

Please clarify which scenario applies, but based on the description, the results are:
- If the sides are 10 and 14, the hypotenuse is approximately **17.2**.
- If the sides are 10 and the hypotenuse is 14, the missing side is approximately **9.8**.