Use the inverse of the tangent ratio to find the approximate angle measure at vertex A. Round your answer to the nearest whole degree. Side BC of the right triangle is 20, Side CA of the right triangle is 25, solve for side BA of the right triangle. m<A=
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.