Answer: 38.66 degrees
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Explanation:
As you stated in problem 4, tan(angle) = opposite/adjacent
We'll use this idea to help find angle Z. First lets set up the proper tangent ratio for this problem
tan(Z) = XY/YZ
tan(Z) = 8/10
tan(Z) = 0.8
To isolate Z, we need to undo the tangent function. We will use the inverse tangent or the arctangent function to do this.
tan(Z) = 0.8
arctan( tan(Z) ) = arctan(0.8)
Z = 38.6598 which is approximate
This rounds to 38.66
