Question

Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)
A right triangle shows the base without any value, the hypotenuse on the right with a value of 30, and the perpendicular side to the base on the left with a value of 20.

Answer 1

To find the unknown side length (the base) in the right triangle, we can use the Pythagorean theorem, which states:

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

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides. In this case, we have:

- Hypotenuse \( c = 30 \)
- One perpendicular side \( a = 20 \)
- The base \( b \) is unknown.

Plugging in the known values, we have:

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

Calculating \( 20^2 \) and \( 30^2 \):

\[
400 + b^2 = 900
\]

To find \( b^2 \), subtract 400 from both sides:

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

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

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

Now, using a calculator or looking up the value of \( \sqrt{5} \approx 2.236 \),

\[
b \approx 10 \times 2.236 \approx 22.36
\]

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

\[
\boxed{22.36}
\]