Answer: s, v, w, & x = 13 y = 20 z = 20 + 13√3
<u>Step-by-step explanation:</u>
First, you need to understand the side lengths of each special triangle in the drawing.
A 45°- 45°- 90° triangle has corresponding sides of a - a - a√2
A 30°- 60°- 90° triangle has corresponding sides of b - b√3 - 2b
The hypotenuse of the 45-45-90 triangle is 13√2, so its legs are 13.
So A F = 13 → s = 13 and w = 13
FB = 13 → x = 13
EC = 13 → v = 13
Since the x-value of C is 20, then the x-value of E is also 20 → y = 20
ED is opposite of the 60° angle of the 30-60-90 triangle so ED is EC√3. Since EC = 13, then ED = 13√3.
AE + ED = AD
20 + 13√3 = AD → z = 20 + 13√3
