Question

choose the correct values for x and y in the right triangle. y = 6 x = 3√2 y = 6√2 x = 3

Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 right - triangle, the ratio of the sides is $1:1:\sqrt{2}$, i.e., if the legs are of length $a$, the hypotenuse $c=a\sqrt{2}$.

Step2: Set up equations

Let the length of each leg be $x$. The hypotenuse is $y$. Given one leg is $3\sqrt{2}$. Since the two legs of a 45 - 45 - 90 triangle are equal, $x = 3\sqrt{2}$. And the hypotenuse $y$ of a 45 - 45 - 90 triangle with leg length $x$ is $y=x\sqrt{2}$. Substituting $x = 3\sqrt{2}$ into the formula for $y$, we get $y=(3\sqrt{2})\times\sqrt{2}=3\times2 = 6$.

Answer:

$x = 3\sqrt{2}$, $y = 6$