Question

Use the equation to find the length of the missing leg measure.



NOTE: Type in numerical answers only to receive credit.

(3 points)
a2+162=202

1. Evaluate the powers: a2+
=400

2. Isolate the variable: a2=

3. Take the square root of both sides: a2−−√=144−−−√

4. The missing side length is a=

Answer 1

Let's solve the equation step by step:

1. **Evaluate the powers**:
\[
a^2 + 162 = 202 \quad \Rightarrow \quad a^2 + 162 = 400
\]
(This is given in your problem, assuming it's the interpretation of your question, but we start from \(a^2 + 162 = 202\))

2. **Isolate the variable**:
\[
a^2 + 162 = 202 \quad \Rightarrow \quad a^2 = 202 - 162
\]
\[
a^2 = 40
\]

3. **Take the square root of both sides**:
\[
a = \sqrt{40}
\]

4. **The missing side length in simplified form**:
\[
a = \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}
\]
If you're looking for a numerical approximation,
\[
a \approx 6.32 \quad (\text{or simply write } a = 6.32 \text{ if numerical output is needed like in other steps})
\]

Thus, the final answers are:
- For step 2, \( a^2 = 40 \)
- For step 4, \( a \) (the missing side length) is approximately \( 6.32 \) or \( 2\sqrt{10} \). If only a single numerical answer is satisfactory, \( 6.32 \) would be acceptable.