Question

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.

Answer 1

is 51 degrees

Answer 2

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