Question

solve for y in the provided triangle. note that the diagram may not be to scale. y = 13 y = 17 y = 25 y = 169

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ for right - triangles, where $c$ is the hypotenuse. Here $a = 5$, $b = 12$, and $c=y$.

Step2: Substitute values

Substitute $a = 5$ and $b = 12$ into the Pythagorean theorem: $5^{2}+12^{2}=y^{2}$.

Step3: Calculate squares

$5^{2}=25$ and $12^{2}=144$, so $25 + 144=y^{2}$, which simplifies to $y^{2}=169$.

Step4: Solve for y

Take the square root of both sides. Since $y$ represents the length of a side of a triangle, we take the positive square root. So $y=\sqrt{169}=13$.

Answer:

$y = 13$