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snow_lady [41]
2 years ago
13

JNZ~ KOA. Find the unknown measures

Mathematics
2 answers:
shepuryov [24]2 years ago
4 0

Answer:

<h2>x = 8.5in, y = 17in, r = 28°, s = 62°</h2>

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}        <em>cross multiply</em>

8x=(4)(17)

8x=68          <em>divide both sides by 8</em>

x=8.5\ in

blagie [28]2 years ago
4 0

Answer:

Circle

Step-by-step explanation:

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