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 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write sin(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → sin(θ)
2. 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)
3. 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 cos(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → cos(θ)
4. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 105 cm, and the hypotenuse is 119 cm. Write sin(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · 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 cos(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → cos(θ)
6. In a right-angled triangle, the side opposite angle θ is 42 cm, the adjacent side is 144 cm, and the hypotenuse is 150 cm. Write cos(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → cos(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 tan(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → tan(θ)
8. 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 tan(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → tan(θ)
9. 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 tan(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → tan(θ)
10. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 36 cm, and the hypotenuse is 39 cm. Write sin(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → sin(θ)
11. 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)
12. 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)
12 questions · Seed 104742 · 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 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 12/20, which simplifies by dividing by 4 to 3/5.
2. 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.
3. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 4/5, which simplifies by dividing by 1 to 4/5.
4. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 105 cm, and the hypotenuse is 119 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 56/119, which simplifies by dividing by 7 to 8/17.
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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 120/136, which simplifies by dividing by 8 to 15/17.
6. In a right-angled triangle, the side opposite angle θ is 42 cm, the adjacent side is 144 cm, and the hypotenuse is 150 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 144/150, which simplifies by dividing by 6 to 24/25.
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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 24/32, which simplifies by dividing by 8 to 3/4.
8. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 9/12, which simplifies by dividing by 3 to 3/4.
9. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 35/120, which simplifies by dividing by 5 to 7/24.
10. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 36 cm, and the hypotenuse is 39 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 15/39, which simplifies by dividing by 3 to 5/13.
11. 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.
12. 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.
12 questions · Seed 104742 · 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 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write sin(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → sin(θ)
2. 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)
3. 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 cos(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → cos(θ)
4. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 105 cm, and the hypotenuse is 119 cm. Write sin(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · 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 cos(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → cos(θ)
6. In a right-angled triangle, the side opposite angle θ is 42 cm, the adjacent side is 144 cm, and the hypotenuse is 150 cm. Write cos(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → cos(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 tan(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → tan(θ)
8. 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 tan(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → tan(θ)
9. 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 tan(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → tan(θ)
10. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 36 cm, and the hypotenuse is 39 cm. Write sin(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → sin(θ)
11. 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)
12. 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)
12 questions · Seed 104742 · 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 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 12/20, which simplifies by dividing by 4 to 3/5.
2. 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.
3. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 4/5, which simplifies by dividing by 1 to 4/5.
4. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 105 cm, and the hypotenuse is 119 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 56/119, which simplifies by dividing by 7 to 8/17.
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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 120/136, which simplifies by dividing by 8 to 15/17.
6. In a right-angled triangle, the side opposite angle θ is 42 cm, the adjacent side is 144 cm, and the hypotenuse is 150 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 144/150, which simplifies by dividing by 6 to 24/25.
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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 24/32, which simplifies by dividing by 8 to 3/4.
8. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 9/12, which simplifies by dividing by 3 to 3/4.
9. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 35/120, which simplifies by dividing by 5 to 7/24.
10. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 36 cm, and the hypotenuse is 39 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 15/39, which simplifies by dividing by 3 to 5/13.
11. 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.
12. 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.
12 questions · Seed 104742 · Age guidance, not curriculum certification