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 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)
2. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write sin(θ) as a simplified fraction.
Opp = 40, Adj = 96, Hyp = 104 · Right Triangle → sin(θ)
3. 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)
4. 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 cos(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → cos(θ)
5. 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)
6. 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)
7. 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)
8. 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)
9. 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 sin(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → sin(θ)
10. 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 cos(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → cos(θ)
11. In a right-angled triangle, the side opposite angle θ is 49 cm, the adjacent side is 168 cm, and the hypotenuse is 175 cm. Write tan(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → tan(θ)
12. 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 sin(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → sin(θ)
12 questions · Seed 42 · 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 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.
2. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 40/104, which simplifies by dividing by 8 to 5/13.
3. 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.
4. 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 cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 24/25, which simplifies by dividing by 1 to 24/25.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 30/78, which simplifies by dividing by 6 to 5/13.
10. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 15/17, which simplifies by dividing by 1 to 15/17.
11. In a right-angled triangle, the side opposite angle θ is 49 cm, the adjacent side is 168 cm, and the hypotenuse is 175 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 49/168, which simplifies by dividing by 7 to 7/24.
12. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 40/85, which simplifies by dividing by 5 to 8/17.
12 questions · Seed 42 · 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 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)
2. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write sin(θ) as a simplified fraction.
Opp = 40, Adj = 96, Hyp = 104 · Right Triangle → sin(θ)
3. 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)
4. 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 cos(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → cos(θ)
5. 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)
6. 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)
7. 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)
8. 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)
9. 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 sin(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → sin(θ)
10. 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 cos(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → cos(θ)
11. In a right-angled triangle, the side opposite angle θ is 49 cm, the adjacent side is 168 cm, and the hypotenuse is 175 cm. Write tan(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → tan(θ)
12. 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 sin(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → sin(θ)
12 questions · Seed 42 · 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 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.
2. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 40/104, which simplifies by dividing by 8 to 5/13.
3. 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.
4. 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 cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 24/25, which simplifies by dividing by 1 to 24/25.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 30/78, which simplifies by dividing by 6 to 5/13.
10. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 15/17, which simplifies by dividing by 1 to 15/17.
11. In a right-angled triangle, the side opposite angle θ is 49 cm, the adjacent side is 168 cm, and the hypotenuse is 175 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 49/168, which simplifies by dividing by 7 to 7/24.
12. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 40/85, which simplifies by dividing by 5 to 8/17.
12 questions · Seed 42 · Age guidance, not curriculum certification