Question

right triangle with lengths of 20 and 30, what is the missing length to the nearest hundreth

Answer 1

To find the missing length of a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

If we denote the two known lengths as \( a = 20 \) and \( b = 30 \), we can find the hypotenuse \( c \) using the formula:

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

Plugging in the values:

\[
c = \sqrt{20^2 + 30^2}
\]
\[
c = \sqrt{400 + 900}
\]
\[
c = \sqrt{1300}
\]
\[
c \approx 36.06
\]

Thus, the length of the hypotenuse, rounded to the nearest hundredth, is approximately **36.06**.

If you were looking for the missing leg (assuming the hypotenuse is 30 and one leg is 20), you would instead rearrange the formula:

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

Then you input the values:

\[
b = \sqrt{30^2 - 20^2}
\]
\[
b = \sqrt{900 - 400}
\]
\[
b = \sqrt{500}
\]
\[
b \approx 22.36
\]

So, if we were trying to find the other leg and assuming the hypotenuse was 30, that length would be approximately **22.36**.