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What is the measure of angle A to the nearest degree if side a equals 490 and side b equals 960?
There is not enough information. Angle A can be anything between 0 and 180 degrees.
If you are talking about a triangle ABC, in which angle C is the right angle then a is the opposite side and b is the adjacent side. tan A = opposite / adjacent
tan A = 490 / 960 = 0.51041666666666666666666666666667
and A = invtan(0.51041666666666666666666666666667) [also called tan-1]
so A = 27.04 degrees
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