Question

find z.
triangle with angles 45°, 45°, 90°, hypotenuse 2 yd, leg z
write your answer in simplest radical form.
blank yards

Explanation:

Step1: Identify triangle type

This is a 45-45-90 isosceles right triangle, so the two legs are equal, and the hypotenuse is $\text{leg} \times \sqrt{2}$.

Step2: Relate hypotenuse to leg

The hypotenuse is 2 yd, let the leg length be $z$. The formula is $2 = z\sqrt{2}$.

Step3: Solve for z

Rearrange to isolate $z$: $z = \frac{2}{\sqrt{2}}$. Rationalize the denominator: $z = \frac{2\sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2}$.

Answer:

$\sqrt{2}$ yards