what are the measures of the acute angles of a right triangle with legs of 6 and 12

Answer 1

tangent A = 12/6 = 2

A = tan^-1 (2) = 63.435 degrees or 1.107 radians

B = tan^-1(6/12) = 90-63.435 = 26.565 degrees or 0.4636 radians

The hypotenuse of the right triangle is the square root of the sum of squares of the 2 legs

square root of 4+1 or square root of 5 = 2.236

You could have calculated the hypotenuse and then calculated the sine or cosine

such as: sinA=1/sqr2

A = sin^-1 (1/sqr2) = 26.56 degrees

B = 90-26.56 = 63.44 degrees

Those are the two angles opposite the 2 legs.

90 degrees is the angle opposite the hypotenuse