Question

solve for the legs of the 45 - 45 - 90 triangle. 45° 5√2 y x a. x = 5 and y = 5 b. x = 5 and y = 5√2 c. x = 5√2 and y = 5 d. x = 5√2 and y = 5√2

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the legs are of equal length and the hypotenuse is $\sqrt{2}$ times the length of a leg. Let the length of each leg be $a$. Then the hypotenuse $c = a\sqrt{2}$.

Step2: Set up equation

We are given that the hypotenuse $c = 5\sqrt{2}$. Since $c=a\sqrt{2}$, we have $a\sqrt{2}=5\sqrt{2}$.

Step3: Solve for $a$

Dividing both sides of the equation $a\sqrt{2}=5\sqrt{2}$ by $\sqrt{2}$, we get $a = 5$. So $x = 5$ and $y = 5$.

Answer:

A. x=5 and y=5