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 tan(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → tan(θ)
2. 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 cos(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → cos(θ)
3. 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)
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 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)
6. 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)
7. 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)
8. 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)
9. 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 tan(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · 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 tan(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → tan(θ)
11. In a right-angled triangle, the side opposite angle θ is 32 cm, the adjacent side is 60 cm, and the hypotenuse is 68 cm. Write cos(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · Right Triangle → cos(θ)
12. 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 tan(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · Right Triangle → tan(θ)
12 questions · Seed 51 · 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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 8/15, which simplifies by dividing by 1 to 8/15.
2. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 36/39, which simplifies by dividing by 3 to 12/13.
3. 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.
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 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.
6. 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.
7. 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.
8. 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.
9. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 15/36, which simplifies by dividing by 3 to 5/12.
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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 40/75, which simplifies by dividing by 5 to 8/15.
11. In a right-angled triangle, the side opposite angle θ is 32 cm, the adjacent side is 60 cm, and the hypotenuse is 68 cm. Write cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 60/68, which simplifies by dividing by 4 to 15/17.
12. 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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 56/105, which simplifies by dividing by 7 to 8/15.
12 questions · Seed 51 · 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 tan(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → tan(θ)
2. 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 cos(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → cos(θ)
3. 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)
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 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)
6. 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)
7. 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)
8. 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)
9. 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 tan(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · 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 tan(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → tan(θ)
11. In a right-angled triangle, the side opposite angle θ is 32 cm, the adjacent side is 60 cm, and the hypotenuse is 68 cm. Write cos(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · Right Triangle → cos(θ)
12. 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 tan(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · Right Triangle → tan(θ)
12 questions · Seed 51 · 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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 8/15, which simplifies by dividing by 1 to 8/15.
2. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 36/39, which simplifies by dividing by 3 to 12/13.
3. 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.
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 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.
6. 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.
7. 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.
8. 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.
9. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 15/36, which simplifies by dividing by 3 to 5/12.
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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 40/75, which simplifies by dividing by 5 to 8/15.
11. In a right-angled triangle, the side opposite angle θ is 32 cm, the adjacent side is 60 cm, and the hypotenuse is 68 cm. Write cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 60/68, which simplifies by dividing by 4 to 15/17.
12. 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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 56/105, which simplifies by dividing by 7 to 8/15.
12 questions · Seed 51 · Age guidance, not curriculum certification