Apply sine, cosine and tangent ratios (SOHCAHTOA) in right-angled triangles and simplify to lowest terms. Review suitability for your learners before teaching.
Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.
Worksheet StudioPractice pack · Ages 16-18
Right-triangle trigonometry (SOHCAHTOA)
Take your time. Show your thinking.
1. In a right-angled triangle, the side opposite angle θ is 10 cm, the adjacent side is 24 cm, and the hypotenuse is 26 cm. Write sin(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → sin(θ)
2. In a right-angled triangle, the side opposite angle θ is 9 cm, the adjacent side is 12 cm, and the hypotenuse is 15 cm. Write cos(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → cos(θ)
3. In a right-angled triangle, the side opposite angle θ is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write cos(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → cos(θ)
4. In a right-angled triangle, the side opposite angle θ is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write sin(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → sin(θ)
5. In a right-angled triangle, the side opposite angle θ is 64 cm, the adjacent side is 120 cm, and the hypotenuse is 136 cm. Write tan(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → tan(θ)
6. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → tan(θ)
7. In a right-angled triangle, the side opposite angle θ is 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write cos(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → cos(θ)
8. In a right-angled triangle, the side opposite angle θ is 18 cm, the adjacent side is 24 cm, and the hypotenuse is 30 cm. Write sin(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → sin(θ)
9. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write cos(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → cos(θ)
10. In a right-angled triangle, the side opposite angle θ is 30 cm, the adjacent side is 72 cm, and the hypotenuse is 78 cm. Write cos(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → cos(θ)
11. In a right-angled triangle, the side opposite angle θ is 25 cm, the adjacent side is 60 cm, and the hypotenuse is 65 cm. Write cos(θ) as a simplified fraction.
Opp = 25, Adj = 60, Hyp = 65 · Right Triangle → cos(θ)
12. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write tan(θ) as a simplified fraction.
Opp = 21, Adj = 72, Hyp = 75 · Right Triangle → tan(θ)
12 questions · Seed 54 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18
Right-triangle trigonometry (SOHCAHTOA)
Answers and reasoning. Review before teaching.
1. In a right-angled triangle, the side opposite angle θ is 10 cm, the adjacent side is 24 cm, and the hypotenuse is 26 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 10/26, which simplifies by dividing by 2 to 5/13.
2. In a right-angled triangle, the side opposite angle θ is 9 cm, the adjacent side is 12 cm, and the hypotenuse is 15 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 12/15, which simplifies by dividing by 3 to 4/5.
3. In a right-angled triangle, the side opposite angle θ is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 12/13, which simplifies by dividing by 1 to 12/13.
4. In a right-angled triangle, the side opposite angle θ is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 5/13, which simplifies by dividing by 1 to 5/13.
5. In a right-angled triangle, the side opposite angle θ is 64 cm, the adjacent side is 120 cm, and the hypotenuse is 136 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 64/120, which simplifies by dividing by 8 to 8/15.
6. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 48/90, which simplifies by dividing by 6 to 8/15.
7. In a right-angled triangle, the side opposite angle θ is 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 32/40, which simplifies by dividing by 8 to 4/5.
8. In a right-angled triangle, the side opposite angle θ is 18 cm, the adjacent side is 24 cm, and the hypotenuse is 30 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 18/30, which simplifies by dividing by 6 to 3/5.
9. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 192/200, which simplifies by dividing by 8 to 24/25.
10. In a right-angled triangle, the side opposite angle θ is 30 cm, the adjacent side is 72 cm, and the hypotenuse is 78 cm. Write cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 72/78, which simplifies by dividing by 6 to 12/13.
11. In a right-angled triangle, the side opposite angle θ is 25 cm, the adjacent side is 60 cm, and the hypotenuse is 65 cm. Write cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 60/65, which simplifies by dividing by 5 to 12/13.
12. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 21/72, which simplifies by dividing by 3 to 7/24.
12 questions · Seed 54 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18
Right-triangle trigonometry (SOHCAHTOA)
Take your time. Show your thinking.
1. In a right-angled triangle, the side opposite angle θ is 10 cm, the adjacent side is 24 cm, and the hypotenuse is 26 cm. Write sin(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → sin(θ)
2. In a right-angled triangle, the side opposite angle θ is 9 cm, the adjacent side is 12 cm, and the hypotenuse is 15 cm. Write cos(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → cos(θ)
3. In a right-angled triangle, the side opposite angle θ is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write cos(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → cos(θ)
4. In a right-angled triangle, the side opposite angle θ is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write sin(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → sin(θ)
5. In a right-angled triangle, the side opposite angle θ is 64 cm, the adjacent side is 120 cm, and the hypotenuse is 136 cm. Write tan(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → tan(θ)
6. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → tan(θ)
7. In a right-angled triangle, the side opposite angle θ is 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write cos(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → cos(θ)
8. In a right-angled triangle, the side opposite angle θ is 18 cm, the adjacent side is 24 cm, and the hypotenuse is 30 cm. Write sin(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → sin(θ)
9. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write cos(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → cos(θ)
10. In a right-angled triangle, the side opposite angle θ is 30 cm, the adjacent side is 72 cm, and the hypotenuse is 78 cm. Write cos(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → cos(θ)
11. In a right-angled triangle, the side opposite angle θ is 25 cm, the adjacent side is 60 cm, and the hypotenuse is 65 cm. Write cos(θ) as a simplified fraction.
Opp = 25, Adj = 60, Hyp = 65 · Right Triangle → cos(θ)
12. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write tan(θ) as a simplified fraction.
Opp = 21, Adj = 72, Hyp = 75 · Right Triangle → tan(θ)
12 questions · Seed 54 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18
Right-triangle trigonometry (SOHCAHTOA)
Answers and reasoning. Review before teaching.
1. In a right-angled triangle, the side opposite angle θ is 10 cm, the adjacent side is 24 cm, and the hypotenuse is 26 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 10/26, which simplifies by dividing by 2 to 5/13.
2. In a right-angled triangle, the side opposite angle θ is 9 cm, the adjacent side is 12 cm, and the hypotenuse is 15 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 12/15, which simplifies by dividing by 3 to 4/5.
3. In a right-angled triangle, the side opposite angle θ is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 12/13, which simplifies by dividing by 1 to 12/13.
4. In a right-angled triangle, the side opposite angle θ is 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 5/13, which simplifies by dividing by 1 to 5/13.
5. In a right-angled triangle, the side opposite angle θ is 64 cm, the adjacent side is 120 cm, and the hypotenuse is 136 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 64/120, which simplifies by dividing by 8 to 8/15.
6. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 48/90, which simplifies by dividing by 6 to 8/15.
7. In a right-angled triangle, the side opposite angle θ is 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 32/40, which simplifies by dividing by 8 to 4/5.
8. In a right-angled triangle, the side opposite angle θ is 18 cm, the adjacent side is 24 cm, and the hypotenuse is 30 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 18/30, which simplifies by dividing by 6 to 3/5.
9. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 192/200, which simplifies by dividing by 8 to 24/25.
10. In a right-angled triangle, the side opposite angle θ is 30 cm, the adjacent side is 72 cm, and the hypotenuse is 78 cm. Write cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 72/78, which simplifies by dividing by 6 to 12/13.
11. In a right-angled triangle, the side opposite angle θ is 25 cm, the adjacent side is 60 cm, and the hypotenuse is 65 cm. Write cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 60/65, which simplifies by dividing by 5 to 12/13.
12. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 21/72, which simplifies by dividing by 3 to 7/24.
12 questions · Seed 54 · Age guidance, not curriculum certification