Questions: Find the length of the third side. If necessary, write in simplest radical form.

Find the length of the third side. If necessary, write in simplest radical form.
Transcript text: Find the length of the third side. If necessary, write in simplest radical form.
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Solution

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Solution Steps

Step 1: Apply the Pythagorean Theorem

We have a right triangle with legs a and b and hypotenuse c. The Pythagorean theorem states that $a^2 + b^2 = c^2$. Let a = $3\sqrt{3}$ and c = 6. We need to find b.

Step 2: Substitute the values

Substitute the given values into the Pythagorean theorem: $(3\sqrt{3})^2 + b^2 = 6^2$.

Step 3: Simplify and solve for b

Simplify the equation: $27 + b^2 = 36$. Subtract 27 from both sides: $b^2 = 9$. Take the square root of both sides: $b = 3$.

Final Answer: 3

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