Question

Use the equation to find the length of the missing leg measure. %C2%A0 NOTE: Type in numerical answers only to receive credit. (3 points) a2+162=202 1. Evaluate the powers:%C2%A0a2+ =400 2. Isolate the variable:%C2%A0a2= 3. Take the square root of both sides:%C2%A0a2−−√=144−−−√ 4. The missing side length is%C2%A0a=

Answer 1

Let's solve the equation step by step.

You were given the equation:

\[
a^2 + 162 = 202
\]

1. **Evaluate the powers**: We need to isolate \(a^2\), which means we'll start by subtracting 162 from both sides:

\[
a^2 = 202 - 162
\]

Calculating the right side:

\[
a^2 = 40
\]

2. **Isolate the variable**: In this case, we have already isolated the variable:

\[
a^2 = 40
\]

3. **Take the square root of both sides**: Now, we take the square root:

\[
a = \sqrt{40}
\]

Simplifying \(\sqrt{40}\):

\[
\sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}
\]

4. **The missing side length**: We can provide the numerical approximation of \(\sqrt{40}\):

\[
a \approx \sqrt{40} \approx 6.32 \text{ (rounded to two decimal places)}
\]

If you are looking for the exact form:

\[
a = 2\sqrt{10}
\]

So if you want the numerical answer:

**The missing side length is approximately** \(6.32\) (if rounding to two decimal places) or leave it in exact form as \(2\sqrt{10}\).