You are given BC and AC, lets find AB by using the Pythagorean theorem:
AB = √(20^2 - 16^2)
AB = √(400-256)
AB = √144
AB = 12
Since the triangles are similar, sin F would be the same as sin C
SinC = Opposite side / hypotenuse
SinC = 12/20, reduces to 3/5
SinF = SinC = 3/5
Then if you need the angle of F:
F = arcsin(3/5) = 36.87 degrees.
Answer:
Sin F = 3/5
Step-by-step explanation:
Since F= C because the triangles are similar
Sin F = Sin C since the triangles are similar
sin C = opposite / hypotenuse
=AB/AC
We know AC =20, but we need to determine AB
Since this is a right triangle
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
sqrt(AB^2) =sqrt(144)
AB = 12
sin C = 12/20
Divide the top and bottom by 4
sin C = 3/5
Sin F = 3/5
