Question

value: 3
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 legs to the hypotenuse is $1:1:\sqrt{2}$. Let the length of each leg be $a$, and the hypotenuse be $c$. Then $c = a\sqrt{2}$.

Step2: Set up equation to solve for leg

We are given that $c = 5\sqrt{2}$. Since $c=a\sqrt{2}$, we set $a\sqrt{2}=5\sqrt{2}$. Dividing both sides of the equation by $\sqrt{2}$, we get $a = 5$. So $x = 5$ and $y = 5$.

Answer:

A. $x = 5$ and $y = 5$