Solve for the remaining sides and angles if possible. α = 62.1°, a = 86, b = 91. Find the values of the smaller β and larger β?

Question

The values I got for the smaller Beta triangle are Beta = 46.62, Gamma= 117.90, and c=125.21 for the hypotenuse length. The values that I got for the larger Beta triangle are Beta = 46.98, Gamma= 70.92, and c=29.75 for the hypotenuse length.

Answer 1

α = 62.1°, a = 86, b = 91.

a/sin α = b/sin β

91 sin 62.1° = 86 sin β

80.42/86 = sin β

0.935116 = sin(β)

The values of the smaller β and larger β:

β = 2 π n+π-sin^(-1)(233779/250000), n element Z

β = 2 π n+sin^(-1)(233779/250000), n element Z

Answer 2

Hint:

sine rule

a/sinA=b/sinB=c/sinC