In △CDE , CD=12 , DE=5 , and m∠E=83∘ . What is m∠D to the nearest tenth of a degree? Enter your answer in the box.
E = 83
5
C 12 D
We have the ambiguous case here
sin C / DE = sin E /CD
sin C / 5 = sin 83 / 12
sin C = 5 * sin 83 / 12
arcsin ( 5 sin 83 / 12) = C = 24.4°
So...in this case D = 180 - 83 - 24.4 = 72.6°
The other possible value for C = 180 - 24 = 156
But adding this to then known angle 83 is more than 180, so we only have one triangle
So angle D = 72.6°