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The measure of angle Z = ______ degrees ( round to the nearest degree)

The measure of angle Z = ______ degrees ( round to the nearest degree)-example-1
User Mahorad
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2 Answers

2 votes
law of cosines

Z = acos( (6.8^2 + 14.7^2 - 9.7^2)/(2×6.8×14.7) )

Z = 32.697 deg = 33 degrees
User Polemon
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4 votes
This is a perfect place to apply the Law of Cosines. We want angle Z and know the length of the side opposite this angle: 9.7.

Law of Cosines is c^2 = a^2 + b^2 - 2ab*cos C

Applied here, we get

9.7^2 = 6.8^2 + 14.7^2 - 2(6.8)(14.7)*cos Z

Then

94.09 = 46.24 + 216.09 - 199.92*cos Z

Grouping the constant terms together:

-167.43 = -199.92*cos Z

Solving for cos Z:

0-.8374 = -cos Z

0.8374 = cos Z

Applying the inverse cosine function: Z = 0.578 radians = 33 degrees
User Vebbie
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5.3k points