Answer:
x = 8.5in, y = 17in, r = 28°, s = 62°
Step-by-step explanation:
If ΔJNZ and ΔKOA are similar, then corresponding sides are in proportion and corresponding angles are congruent.
We have the proportion:
[tex]\dfrac{JN}{KO}=\dfrac{NZ}{OA}=\dfrac{ZJ}{AK}[/tex]
and equations:
[tex]m\angle N=m\angle O=90^o\\m\angle Z=m\angle A=28^o\\m\angle J=m\angle K=62^o[/tex]
We have:
[tex]JN=8\ in,\ NZ=15\ in,\ KO=4\ in,\ AK=x\ in,\ ZJ=y\ in[/tex]
For y we must use the Pythagorean theorem:
[tex]ZJ^2=JN^2+NZ^2\\\\y^2=8^2+15^2\\\\y^2=64+225\\\\y^2=289\to y=\sqrt{289}\\\\y=17\ in[/tex]
[tex]\dfrac{JN}{KO}=\dfrac{ZJ}{AK}\to\dfrac{8}{4}=\dfrac{17}{x}[/tex] cross multiply
[tex]8x=(4)(17)[/tex]
[tex]8x=68[/tex] divide both sides by 8
[tex]x=8.5\ in[/tex]
