Question

what is the length of leg s of the triangle below? 45° 8√2 s 90° 45° a. 2 b. 4√2 c. 8 d. 1 e. 8√2 f. 4.2

Explanation:

Step1: Identify triangle type

This is a 45 - 45 - 90 right - triangle. 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 $c$ is $\sqrt{2}$ times the length of a leg $a$ (i.e., $c = a\sqrt{2}$).

Step2: Set up equation

Let the length of the leg be $s$. The hypotenuse $c = 8\sqrt{2}$. Since $c=s\sqrt{2}$, we have the equation $s\sqrt{2}=8\sqrt{2}$.

Step3: Solve for $s$

Divide both sides of the equation $s\sqrt{2}=8\sqrt{2}$ by $\sqrt{2}$. So, $s = 8$.

Answer:

C. 8