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 13-15
Right-triangle trigonometry (SOHCAHTOA)
Take your time. Show your thinking.
1. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 20 cm, and the hypotenuse is 25 cm. Write sin(θ) as a simplified fraction.
Opp = 15, Adj = 20, Hyp = 25 · Right Triangle → sin(θ)
2. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 28 cm, and the hypotenuse is 35 cm. Write sin(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → sin(θ)
3. 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 tan(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → tan(θ)
4. In a right-angled triangle, the side opposite angle θ is 6 cm, the adjacent side is 8 cm, and the hypotenuse is 10 cm. Write sin(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · 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 cos(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → cos(θ)
6. 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 cos(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → cos(θ)
7. In a right-angled triangle, the side opposite angle θ is 16 cm, the adjacent side is 30 cm, and the hypotenuse is 34 cm. Write cos(θ) as a simplified fraction.
Opp = 16, Adj = 30, Hyp = 34 · Right Triangle → cos(θ)
8. 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)
9. In a right-angled triangle, the side opposite angle θ is 6 cm, the adjacent side is 8 cm, and the hypotenuse is 10 cm. Write cos(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → cos(θ)
10. In a right-angled triangle, the side opposite angle θ is 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write cos(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → cos(θ)
11. 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)
12. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 84 cm, and the hypotenuse is 91 cm. Write sin(θ) as a simplified fraction.
Opp = 35, Adj = 84, Hyp = 91 · Right Triangle → sin(θ)
12 questions · Seed 57 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 13-15
Right-triangle trigonometry (SOHCAHTOA)
Answers and reasoning. Review before teaching.
1. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 20 cm, and the hypotenuse is 25 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 15/25, which simplifies by dividing by 5 to 3/5.
2. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 28 cm, and the hypotenuse is 35 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 21/35, which simplifies by dividing by 7 to 3/5.
3. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 7/24, which simplifies by dividing by 1 to 7/24.
4. In a right-angled triangle, the side opposite angle θ is 6 cm, the adjacent side is 8 cm, and the hypotenuse is 10 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 6/10, which simplifies by dividing by 2 to 3/5.
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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 90/102, which simplifies by dividing by 6 to 15/17.
6. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 24/30, which simplifies by dividing by 6 to 4/5.
7. In a right-angled triangle, the side opposite angle θ is 16 cm, the adjacent side is 30 cm, and the hypotenuse is 34 cm. Write cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 30/34, which simplifies by dividing by 2 to 15/17.
8. 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.
9. In a right-angled triangle, the side opposite angle θ is 6 cm, the adjacent side is 8 cm, and the hypotenuse is 10 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 8/10, which simplifies by dividing by 2 to 4/5.
10. In a right-angled triangle, the side opposite angle θ is 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 96/100, which simplifies by dividing by 4 to 24/25.
11. 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.
12. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 84 cm, and the hypotenuse is 91 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 35/91, which simplifies by dividing by 7 to 5/13.
12 questions · Seed 57 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 13-15
Right-triangle trigonometry (SOHCAHTOA)
Take your time. Show your thinking.
1. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 20 cm, and the hypotenuse is 25 cm. Write sin(θ) as a simplified fraction.
Opp = 15, Adj = 20, Hyp = 25 · Right Triangle → sin(θ)
2. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 28 cm, and the hypotenuse is 35 cm. Write sin(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → sin(θ)
3. 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 tan(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → tan(θ)
4. In a right-angled triangle, the side opposite angle θ is 6 cm, the adjacent side is 8 cm, and the hypotenuse is 10 cm. Write sin(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · 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 cos(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → cos(θ)
6. 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 cos(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → cos(θ)
7. In a right-angled triangle, the side opposite angle θ is 16 cm, the adjacent side is 30 cm, and the hypotenuse is 34 cm. Write cos(θ) as a simplified fraction.
Opp = 16, Adj = 30, Hyp = 34 · Right Triangle → cos(θ)
8. 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)
9. In a right-angled triangle, the side opposite angle θ is 6 cm, the adjacent side is 8 cm, and the hypotenuse is 10 cm. Write cos(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → cos(θ)
10. In a right-angled triangle, the side opposite angle θ is 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write cos(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → cos(θ)
11. 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)
12. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 84 cm, and the hypotenuse is 91 cm. Write sin(θ) as a simplified fraction.
Opp = 35, Adj = 84, Hyp = 91 · Right Triangle → sin(θ)
12 questions · Seed 57 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 13-15
Right-triangle trigonometry (SOHCAHTOA)
Answers and reasoning. Review before teaching.
1. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 20 cm, and the hypotenuse is 25 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 15/25, which simplifies by dividing by 5 to 3/5.
2. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 28 cm, and the hypotenuse is 35 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 21/35, which simplifies by dividing by 7 to 3/5.
3. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 7/24, which simplifies by dividing by 1 to 7/24.
4. In a right-angled triangle, the side opposite angle θ is 6 cm, the adjacent side is 8 cm, and the hypotenuse is 10 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 6/10, which simplifies by dividing by 2 to 3/5.
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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 90/102, which simplifies by dividing by 6 to 15/17.
6. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 24/30, which simplifies by dividing by 6 to 4/5.
7. In a right-angled triangle, the side opposite angle θ is 16 cm, the adjacent side is 30 cm, and the hypotenuse is 34 cm. Write cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 30/34, which simplifies by dividing by 2 to 15/17.
8. 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.
9. In a right-angled triangle, the side opposite angle θ is 6 cm, the adjacent side is 8 cm, and the hypotenuse is 10 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 8/10, which simplifies by dividing by 2 to 4/5.
10. In a right-angled triangle, the side opposite angle θ is 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 96/100, which simplifies by dividing by 4 to 24/25.
11. 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.
12. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 84 cm, and the hypotenuse is 91 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 35/91, which simplifies by dividing by 7 to 5/13.
12 questions · Seed 57 · Age guidance, not curriculum certification