Question

find the length of the missing leg in the provided triangle. note that the diagram may not be to scale. 9, $sqrt{27}$, 3, 27

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a,b$ are the legs. Let the missing leg be $x$. Given $c = 15$ and one leg $b = 12$. Then $x^{2}+12^{2}=15^{2}$.

Step2: Rearrange the equation to solve for $x$

$x^{2}=15^{2}-12^{2}$. Calculate $15^{2}=225$ and $12^{2}=144$. So $x^{2}=225 - 144=81$.

Step3: Find the value of $x$

Take the square root of both sides. Since $x$ represents the length of a side of a triangle, we take the positive square root. $x=\sqrt{81}=9$.

Answer:

9