Question

question
find the length of the third side. if necessary, write in simplest radical form.
answer attempt 1 out of 2
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Explanation:

Step1: Identify the triangle type

The triangle is a right triangle, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 4\), \(b=\sqrt{33}\), and \(c\) is the hypotenuse (the third side we need to find).

Step2: Apply the Pythagorean theorem

Substitute the values into the formula: \(c^2=4^2 + (\sqrt{33})^2\). Calculate each term: \(4^2 = 16\) and \((\sqrt{33})^2 = 33\). Then add them: \(c^2=16 + 33 = 49\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{49}=7\).

Answer:

7