Answer:
3/5
Step-by-step explanation:
ABC ≅DEF
B = 90 degrees
BC = 16 and AC = 20
That means
A=D
B=E
C=F
The scale factor is 1/3
AB = 3 DE
BC = 3 EF
AC = 3 DF
We know that trig functions only depend on similarity not congruence so
sin C = sin F
Using the Pythagorean theorem we can find AB
AB^2 +BC^2 = AC^2
AB^2 +16^2 = 20^2
AB^2 +256 = 400
Subtract 256 from each side
AB^2 +256-256 = 400-256
AB^2 =144
Take the square root of each side
AB = sqrt144
AB = 12
sin C = opposite side /hypotenuse
opposite side is AB hypotenuse = AC
sin C = AB/AC
sin C = 12/20
sin C = 3/5
Sin C = sin F = 3/5
