Answer:
[tex]3 \sqrt{17}[/tex]
Step-by-step explanation:
The given triangle is a right triangle. Therefore, we can use Pythagoras Theorem to find the measure of the third side.
Pythagoras Theorem
[tex]a^2+b^2=c^2[/tex]
where:
- a and b are the legs of the right triangle
- c is the hypotenuse (longest side) of the right triangle
From inspection of the given triangle:
To calculate the measure of the third side "b", substitute the given values into the formula and solve for b:
[tex]\begin{aligned}a^2+b^2 & = c^2\\\implies 4^2+b^2 & = 13^2\\16+b^2 & = 169\\16+b^2-16 & = 169-16 \\b^2 & = 153\\\sqrt{b^2} & =\sqrt{153}\\b & = \sqrt{9 \cdot 17}\\b & = \sqrt{9}\sqrt{17}\\b & = 3\sqrt{17}\end{aligned}[/tex]
Therefore, the measure of the third side of the given right triangle in simplest radical form is [tex]3 \sqrt{17}[/tex].
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