Question

JNZ~ KOA. Find the unknown measures

Answer 1

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:

$\dfrac{JN}{KO}=\dfrac{NZ}{OA}=\dfrac{ZJ}{AK}$

and equations:

$m\angle N=m\angle O=90^o\\m\angle Z=m\angle A=28^o\\m\angle J=m\angle K=62^o$

We have:

$JN=8\ in,\ NZ=15\ in,\ KO=4\ in,\ AK=x\ in,\ ZJ=y\ in$

For y we must use the Pythagorean theorem:

$ZJ^2=JN^2+NZ^2\\\\y^2=8^2+15^2\\\\y^2=64+225\\\\y^2=289\to y=\sqrt{289}\\\\y=17\ in$

$\dfrac{JN}{KO}=\dfrac{ZJ}{AK}\to\dfrac{8}{4}=\dfrac{17}{x}$        cross multiply

$8x=(4)(17)$

$8x=68$          divide both sides by 8

$x=8.5\ in$

Answer 2

Answer:

Circle

Step-by-step explanation: