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In triangle XYZ, if angle Y = 109°, side z = 6.4 inches, and side y = 6.2 inches, find all possible values of angle Z, to the nearest tenth of a degree.

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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