Answer:
Sin F = 0.6
Step-by-step explanation:
From triangle ABC, applying Pythagoras theorem to determine the length AB;
[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]
[tex]/AC/^{2}[/tex] = [tex]/BC/^{2}[/tex] + [tex]/AB/^{2}[/tex]
[tex]/20/^{2}[/tex] = [tex]/16/^{2}[/tex] + [tex]/AB/^{2}[/tex]
400 = 256 + [tex]/AB/^{2}[/tex]
[tex]/AB/^{2}[/tex] = 400 - 256
= 144
AB = [tex]\sqrt{144}[/tex]
= 12
AB = 12, AC = 20, BC = 16
Therefore since ΔABC ≅ ΔDEF, and each side of triangle DEF is [tex]\frac{1}{3}[/tex] the length of the corresponding side of triangle ABC.
Then,
DE = [tex]\frac{1}{3}[/tex]AB = [tex]\frac{1}{3}[/tex] x 12
= 4
EF = [tex]\frac{1}{3}[/tex]BC = [tex]\frac{1}{3}[/tex] x 16
= [tex]\frac{16}{3}[/tex]
DF = [tex]\frac{1}{3}[/tex]AC = [tex]\frac{1}{3}[/tex] x 20
= [tex]\frac{20}{3}[/tex]
Then, applying trigonometric function to ΔDEF, we have;
Sin F = [tex]\frac{opposite}{hypotenuse}[/tex]
= [tex]\frac{DE}{DF}[/tex]
= 4 ÷ [tex]\frac{20}{3}[/tex]
= 4 x [tex]\frac{3}{20}[/tex]
= [tex]\frac{3}{5}[/tex]
Sin F = 0.6
