Question

special right triangle #5b unique id:1045 this is the only question in this section. question solve for x and y 3√5 x 45° y

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 special right - triangle. In a 45 - 45 - 90 triangle, the legs are congruent, so $x = y$.

Step2: Apply the Pythagorean theorem or ratio

The ratio of the sides in a 45 - 45 - 90 triangle is $a:a:a\sqrt{2}$, where $a$ is the length of each leg and $a\sqrt{2}$ is the length of the hypotenuse. Given the hypotenuse $c = 3\sqrt{5}$, and $c=a\sqrt{2}$. So $3\sqrt{5}=a\sqrt{2}$.

Step3: Solve for $a$ (which is $x$ and $y$)

We have $a=\frac{3\sqrt{5}}{\sqrt{2}}$. Rationalize the denominator: $a=\frac{3\sqrt{5}\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{3\sqrt{10}}{2}$. So $x = y=\frac{3\sqrt{10}}{2}$.

Answer:

$x=\frac{3\sqrt{10}}{2},y=\frac{3\sqrt{10}}{2}$