Question

z = 10, what are x and y? x = choose your answer... , y = choose your answer...

Explanation:

Step1: Identify Triangle Type

This is a right - isosceles triangle (one angle 90°, one angle 45°, so the third angle is also 45°). In a right - isosceles triangle, the two legs (x and z) are equal. Given \(z = 10\), so \(x=z = 10\).

Step2: Calculate Hypotenuse \(y\)

Use the Pythagorean theorem \(y=\sqrt{x^{2}+z^{2}}\). Since \(x = z=10\), then \(y=\sqrt{10^{2}+10^{2}}=\sqrt{100 + 100}=\sqrt{200}=10\sqrt{2}\). Also, in a 45 - 45 - 90 triangle, the hypotenuse is leg\(\times\sqrt{2}\), so \(y = 10\sqrt{2}\).

Answer:

\(x = 10\), \(y=10\sqrt{2}\) (or approximately \(14.14\) if a decimal approximation is preferred)