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To find the length of side BA, we can use the Pythagorean theorem.
BA^2 + CA^2 = BC^2
BA^2 + 25^2 = 20^2
BA^2 + 625 = 400
BA^2 = 400 - 625
BA^2 = 225
BA = √225
BA = 15
Now, we can use the tangent ratio to find the angle measure at vertex A.
tan(A) = opposite / adjacent
tan(A) = 20 / 15
tan(A) = 4/3
To find angle A, we take the inverse tangent (arctan) of 4/3:
A ≈ arctan(4/3)
A ≈ 53.13 degrees
Rounded to the nearest whole degree, m<A = 53 degrees.