Given Info: Angle C = 90 degrees Angle B = 27 degrees side c = 15
What is needed to be found: Angle A, side a, side b
Finding side a cos(angle) = adjacent/hypotenuse cos(B) = BC/AB cos(B) = a/15 cos(27) = a/15 15*cos(27) = a 13.3650978628256 = a a = 13.3650978628256 a = 13.4
Finding side b Using the pythagorean theorem a^2 + b^2 = c^2 (13.3650978628256)^2 + b^2 = 15^2 178.625840882906 + b^2 = 225 178.625840882906 + b^2 - 178.625840882906 = 225 - 178.625840882906 b^2 = 46.374159117094 sqrt(b^2) = sqrt(46.374159117094) b = 6.809857496093 b = 6.8
Finding angle A sin(angle) = opposite/hypotenuse sin(A) = BC/AB sin(A) = a/c sin(A) = 13.3650978628256/15 sin(A) = 0.89100652418838 arcsin(sin(A)) = arcsin(0.89100652418838) A = 63.0000000000016 A = 63
