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 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 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)
3. 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)
4. 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)
5. 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)
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 tan(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → tan(θ)
7. 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)
8. 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 tan(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → tan(θ)
9. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write tan(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → tan(θ)
10. 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 sin(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · Right Triangle → sin(θ)
11. In a right-angled triangle, the side opposite angle θ is 24 cm, the adjacent side is 45 cm, and the hypotenuse is 51 cm. Write tan(θ) as a simplified fraction.
Opp = 24, Adj = 45, Hyp = 51 · Right Triangle → tan(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 tan(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → tan(θ)
12 questions · Seed 104741 · 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 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 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.
3. 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.
4. 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.
5. 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.
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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 7/24, which simplifies by dividing by 1 to 7/24.
7. 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.
8. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 6/8, which simplifies by dividing by 2 to 3/4.
9. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 56/192, which simplifies by dividing by 8 to 7/24.
10. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 32/68, which simplifies by dividing by 4 to 8/17.
11. In a right-angled triangle, the side opposite angle θ is 24 cm, the adjacent side is 45 cm, and the hypotenuse is 51 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 24/45, which simplifies by dividing by 3 to 8/15.
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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 10/24, which simplifies by dividing by 2 to 5/12.
12 questions · Seed 104741 · 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 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 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)
3. 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)
4. 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)
5. 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)
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 tan(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → tan(θ)
7. 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)
8. 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 tan(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → tan(θ)
9. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write tan(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → tan(θ)
10. 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 sin(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · Right Triangle → sin(θ)
11. In a right-angled triangle, the side opposite angle θ is 24 cm, the adjacent side is 45 cm, and the hypotenuse is 51 cm. Write tan(θ) as a simplified fraction.
Opp = 24, Adj = 45, Hyp = 51 · Right Triangle → tan(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 tan(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → tan(θ)
12 questions · Seed 104741 · 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 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 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.
3. 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.
4. 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.
5. 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.
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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 7/24, which simplifies by dividing by 1 to 7/24.
7. 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.
8. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 6/8, which simplifies by dividing by 2 to 3/4.
9. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 56/192, which simplifies by dividing by 8 to 7/24.
10. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 32/68, which simplifies by dividing by 4 to 8/17.
11. In a right-angled triangle, the side opposite angle θ is 24 cm, the adjacent side is 45 cm, and the hypotenuse is 51 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 24/45, which simplifies by dividing by 3 to 8/15.
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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 10/24, which simplifies by dividing by 2 to 5/12.
12 questions · Seed 104741 · Age guidance, not curriculum certification