In 𝛥𝐷𝐸𝐹, ∠𝐸 = 43∘, 𝑒 = 12, and 𝑓 = 16. Determine the possible value(s) of ∠𝐹.

Answer 1

Use law of sines

b/SinB = a/SinA

we can sub in your angle names

fSinF=eSinE

16SinF=12Sin43. Solve for F

SinF = (12sin43)/16

sin-1 sinF = sin-1 (12sin43)/16 use calculator

Angle F = 30.8 degrees