Answer:
[tex]a=5 \sqrt{7}[/tex]
Step-by-step explanation:
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle:
[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
Given:
Substitute the given values into the formula and solve for a:
[tex]\begin{aligned}a^2+b^2 & = c^2 \\\implies a^2+9^2 & =16^2\\a^2+81 & =256\\a^2+81-81 & =256-81\\a^2 & =175\\\sqrt{a^2} & =\sqrt{175}\\a & =\sqrt{25 \cdot 7}\\& = \sqrt{25}\sqrt{7}\\& =5\sqrt{7}\end{aligned}[/tex]
Therefore, the measure of the third side of the given right triangle is [tex]5 \sqrt{7}[/tex]
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