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horrorfan [7]
3 years ago
10

The law of cosines is used to find the measure of Z.

Mathematics
2 answers:
Vlad [161]3 years ago
4 0

we know that

The formula of the law of cosines is

z^{2}=a^{2} +b^{2}-2*a*b*cos (Z)

in this problem we have

16^{2}=18^{2} +19^{2}-2*18*19*cos (Z)\\256=324+361-684*cos (Z)\\256=685-684*cos (Z)\\-429=-684*cos (Z)\\\\cos (Z)=\frac{429}{684}\\\\ \\Z=arc\ cos(\frac{429}{684})\\\\\\Z= 51.157

Round to the nearest whole degree

Z=51 degrees

therefore

<u>the answer is</u>

51 degrees

NeX [460]3 years ago
4 0

Answer:

is 51 degrees

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