2016-12-14 10:13 - Free Printable

It looks like you're working on a math worksheet involving the Pythagorean Theorem, which is used to find the missing side of a right triangle. The formula is:

$$
a^2 + b^2 = c^2
$$

Where:
- $a$ and $b$ are the legs of the right triangle,
- $c$ is the hypotenuse (the longest side, opposite the right angle).

The worksheet has problems where you’re given two sides and asked to find the third. Some of the answers involve square roots, and there’s a matching section with approximations (like $\sqrt{67} \approx 8.19$, etc.).

However, your image shows only part of the worksheet, and the specific problem you're asking about isn't fully visible. But based on what's shown, here’s how you'd solve one of these types of problems.

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Example: Solve for $c$ when $a = 4$, $b = 9$

Using the Pythagorean Theorem:

$$
c^2 = a^2 + b^2 = 4^2 + 9^2 = 16 + 81 = 97
$$

$$
c = \sqrt{97} \approx 9.85
$$

So, $c \approx 9.85$. You might match this to an answer choice like T if it says $\sqrt{97} \approx 9.8$.

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Another Example: Solve for $a$ when $b = 12$, $c = 13$

$$
a^2 = c^2 - b^2 = 13^2 - 12^2 = 169 - 144 = 25
$$

$$
a = \sqrt{25} = 5
$$

So, $a = 5$, which matches option N: $\sqrt{25} = 5$.

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General Steps:

1. Identify which side is missing: leg ($a$ or $b$) or hypotenuse ($c$).
2. Plug known values into $a^2 + b^2 = c^2$.
3. Solve for the unknown.
4. Simplify the square root if possible, or use approximation from the key.

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If you can describe or clarify the exact problem you’re stuck on (e.g., “Problem #2: $a=4$, $b=9$, find $c$”), I can walk you through it step-by-step.

Let me know!