Apply sine, cosine and tangent ratios (SOHCAHTOA) in right-angled triangles and simplify to lowest terms. Review suitability for your learners before teaching.
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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 8 cm, the adjacent side is 15 cm, and the hypotenuse is 17 cm. Write sin(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → sin(θ)
2. 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 cos(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → cos(θ)
3. 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 sin(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → sin(θ)
4. In a right-angled triangle, the side opposite angle θ is 14 cm, the adjacent side is 48 cm, and the hypotenuse is 50 cm. Write sin(θ) as a simplified fraction.
Opp = 14, Adj = 48, Hyp = 50 · Right Triangle → sin(θ)
5. 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 sin(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → sin(θ)
6. In a right-angled triangle, the side opposite angle θ is 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write sin(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → sin(θ)
7. In a right-angled triangle, the side opposite angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm. Write sin(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → sin(θ)
8. 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)
9. 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 tan(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → tan(θ)
10. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write cos(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → cos(θ)
11. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write tan(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → tan(θ)
12. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 120 cm, and the hypotenuse is 125 cm. Write sin(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → sin(θ)
12 questions · Seed 58 · 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 8 cm, the adjacent side is 15 cm, and the hypotenuse is 17 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 8/17, which simplifies by dividing by 1 to 8/17.
2. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 120/136, which simplifies by dividing by 8 to 15/17.
3. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 24/40, which simplifies by dividing by 8 to 3/5.
4. In a right-angled triangle, the side opposite angle θ is 14 cm, the adjacent side is 48 cm, and the hypotenuse is 50 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 14/50, which simplifies by dividing by 2 to 7/25.
5. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 48/102, which simplifies by dividing by 6 to 8/17.
6. In a right-angled triangle, the side opposite angle θ is 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 7/25, which simplifies by dividing by 1 to 7/25.
7. In a right-angled triangle, the side opposite angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 3/5, which simplifies by dividing by 1 to 3/5.
8. 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.
9. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 24/32, which simplifies by dividing by 8 to 3/4.
10. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 75/85, which simplifies by dividing by 5 to 15/17.
11. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 40/75, which simplifies by dividing by 5 to 8/15.
12. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 120 cm, and the hypotenuse is 125 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 35/125, which simplifies by dividing by 5 to 7/25.
12 questions · Seed 58 · 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 8 cm, the adjacent side is 15 cm, and the hypotenuse is 17 cm. Write sin(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → sin(θ)
2. 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 cos(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → cos(θ)
3. 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 sin(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → sin(θ)
4. In a right-angled triangle, the side opposite angle θ is 14 cm, the adjacent side is 48 cm, and the hypotenuse is 50 cm. Write sin(θ) as a simplified fraction.
Opp = 14, Adj = 48, Hyp = 50 · Right Triangle → sin(θ)
5. 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 sin(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → sin(θ)
6. In a right-angled triangle, the side opposite angle θ is 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write sin(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → sin(θ)
7. In a right-angled triangle, the side opposite angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm. Write sin(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → sin(θ)
8. 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)
9. 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 tan(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → tan(θ)
10. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write cos(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → cos(θ)
11. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write tan(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → tan(θ)
12. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 120 cm, and the hypotenuse is 125 cm. Write sin(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → sin(θ)
12 questions · Seed 58 · 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 8 cm, the adjacent side is 15 cm, and the hypotenuse is 17 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 8/17, which simplifies by dividing by 1 to 8/17.
2. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 120/136, which simplifies by dividing by 8 to 15/17.
3. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 24/40, which simplifies by dividing by 8 to 3/5.
4. In a right-angled triangle, the side opposite angle θ is 14 cm, the adjacent side is 48 cm, and the hypotenuse is 50 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 14/50, which simplifies by dividing by 2 to 7/25.
5. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 48/102, which simplifies by dividing by 6 to 8/17.
6. In a right-angled triangle, the side opposite angle θ is 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 7/25, which simplifies by dividing by 1 to 7/25.
7. In a right-angled triangle, the side opposite angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 3/5, which simplifies by dividing by 1 to 3/5.
8. 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.
9. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 24/32, which simplifies by dividing by 8 to 3/4.
10. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 75/85, which simplifies by dividing by 5 to 15/17.
11. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 40/75, which simplifies by dividing by 5 to 8/15.
12. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 120 cm, and the hypotenuse is 125 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 35/125, which simplifies by dividing by 5 to 7/25.
12 questions · Seed 58 · Age guidance, not curriculum certification