Final Answer:
First triangle (sides 3, 4, 5):
sin θ = 4/5
cos θ = 3/5
tan θ = 4/3
csc θ = 5/4
sec θ = 5/3
cot θ = 3/4
Second triangle (sides 8, ?, 11 — right triangle, so missing side = √(11² − 8²) = √(121 − 64) = √57):
sin θ = √57 / 11
cos θ = 8 / 11
tan θ = √57 / 8
csc θ = 11 / √57
sec θ = 11 / 8
cot θ = 8 / √57
Third triangle (sides 9, ?, 13 — right triangle, so missing side = √(13² − 9²) = √(169 − 81) = √88 = 2√22):
sin θ = 2√22 / 13
cos θ = 9 / 13
tan θ = 2√22 / 9
csc θ = 13 / (2√22)
sec θ = 13 / 9
cot θ = 9 / (2√22)
Parent Tip: Review the logic above to help your child master the concept of geometry sohcahtoa worksheet.