The law of cosines is used to find the measure of Z. To the nearest whole degree, what is the measure of Z? 41º 47º 51º 57º

Question

asked Jan 4, 2020 232k views

2 Answers

Mms · Answer 1 · 2020-01-11T00:56:59+0000

Answer:

C.
$Z=51^(\circ)$

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:

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

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

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

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

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

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

$0.627192982456=\text{cos}(Z)$

$\text{cos}(Z)=0.627192982456$

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.