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VashaNatasha [74]
3 years ago
14

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

Mathematics
2 answers:
TEA [102]3 years ago
7 0

Answer:

C. 51º

Step-by-step explanation:

Shtirlitz [24]3 years ago
6 0

Answer:

C. Z=51^{\circ}

Step-by-step explanation:

We have been given a triangle. We are asked to find the measure of angle Z using Law of cosines.

Law of cosines: c^2=a^2+b^2-2ab\cdot \text{cos}(C), where, a, b and c are sides opposite to angles A, B and C respectively.

Upon substituting our given values in law of cosines, we will get:

16^2=19^2+18^2-2(19)(18)\cdot \text{cos}(Z)

256=361+324-684\cdot \text{cos}(Z)

256=685-684\cdot \text{cos}(Z)

256-685=685-685-684\cdot \text{cos}(Z)

-429=-684\cdot \text{cos}(Z)

\frac{-429}{-684}=\frac{-684\cdot \text{cos}(Z)}{-684}

0.627192982456=\text{cos}(Z)

\text{cos}(Z)=0.627192982456

Now, we will use inverse cosine or arc-cos to solve for angle Z as:

Z=\text{cos}^{-1}(0.627192982456)

Z=51.1566718^{\circ}

Z\approx 51^{\circ}

Therefore, the measure of angle Z is approximately 51 degrees.

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