Question

Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)
20^2+x^2=30^2

Answer 1

To find the unknown side length \( x \) in the triangle, we start with the given equation:

\[
20^2 + x^2 = 30^2
\]

Calculating the squares:

\[
20^2 = 400
\]
\[
30^2 = 900
\]

Substituting these values into the equation gives:

\[
400 + x^2 = 900
\]

Next, we isolate \( x^2 \) by subtracting 400 from both sides:

\[
x^2 = 900 - 400
\]
\[
x^2 = 500
\]

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

\[
x = \sqrt{500}
\]

Simplifying \( \sqrt{500} \):

\[
\sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5}
\]

Now, using the approximate value of \( \sqrt{5} \approx 2.236 \):

\[
x \approx 10 \times 2.236 = 22.36
\]

Thus, rounding to the nearest hundredth, the length of the unknown side \( x \) is:

\[
\boxed{22.36}
\]