Answer: 37.8579
This value is approximate and rounded to four decimal places
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Explanation:
The tangent function is being applied to some unknown angle x. To isolate x, we undo whatever tangent is doing. So we apply the inverse function. Specifically the inverse tangent function. This is also known as "arctangent" and your calculator most likely shows it as a button with a "-1" exponent above the "tan"
So apply the arctangent to both sides to get
tan(x) = 0.7773
arctan(tan(x)) = arctan(0.7773)
x = 37.8579
My calculator is in degree mode.
