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

162 = 182 + 192 – 2(18)(19)cos(Z)

256 = 324 + 361 – (684)cos(Z)

256 = 685 – (684)cos(Z)

–429 = –(684)cos(Z)


To the nearest whole degree, the measure of Z is _______ degrees.

User Gary Qian
by
8.1k points

2 Answers

1 vote

Answer:

is 51 degrees

User Alan Hensel
by
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3 votes

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)=(429)/(684)\\\\ \\Z=arc\ cos((429)/(684))\\\\\\Z= 51.157

Round to the nearest whole degree

Z=51 degrees

therefore

the answer is

51 degrees

User Amin
by
8.5k points
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