Answer :
Final answer:
The question is asking for the possible values of angle Z in a non-right triangle XYZ using the Law of Sines. Given that Y = 109°, z = 6.4 inches, and y = 6.2 inches, we set up the equation sinZ/z = sinY/y and solve for Z to find its possible values.
Explanation:
The subject of the question is the use of the Law of Sines in trigonometry to calculate the possible values of an angle in a non-right triangle (triangle XYZ). Given that Y = 109°, z = 6.4 inches, and y = 6.2 inches, the Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. This can be written as
a/sinA = b/sinB = c/sinC
So in this case, we can set up the following equation to solve for angle Z:
sinZ/z = sinY/y
Substituting the given values:
sinZ/6.4 = sin109°/6.2
We can solve this equation for Z, which will provide us with the possible values of Z to the nearest 10th of a degree.
Learn more about Law of Sines here:
https://brainly.com/question/12652434
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