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 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write sin(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → sin(θ)
2. 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)
3. 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 cos(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → cos(θ)
4. 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)
5. 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)
6. 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 cos(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · 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 sin(θ) as a simplified fraction.
Opp = 16, Adj = 30, Hyp = 34 · Right Triangle → sin(θ)
8. 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)
9. 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)
10. In a right-angled triangle, the side opposite angle θ is 20 cm, the adjacent side is 48 cm, and the hypotenuse is 52 cm. Write cos(θ) as a simplified fraction.
Opp = 20, Adj = 48, Hyp = 52 · 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 sin(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → sin(θ)
12. 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 sin(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → sin(θ)
12 questions · Seed 60 · 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 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 28/100, which simplifies by dividing by 4 to 7/25.
2. 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.
3. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 24/26, which simplifies by dividing by 2 to 12/13.
4. 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.
5. 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.
6. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 105/119, which simplifies by dividing by 7 to 15/17.
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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 16/34, which simplifies by dividing by 2 to 8/17.
8. 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.
9. 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.
10. In a right-angled triangle, the side opposite angle θ is 20 cm, the adjacent side is 48 cm, and the hypotenuse is 52 cm. Write cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 48/52, which simplifies by dividing by 4 to 12/13.
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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 49/175, which simplifies by dividing by 7 to 7/25.
12. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 9/15, which simplifies by dividing by 3 to 3/5.
12 questions · Seed 60 · 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 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write sin(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → sin(θ)
2. 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)
3. 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 cos(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → cos(θ)
4. 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)
5. 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)
6. 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 cos(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · 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 sin(θ) as a simplified fraction.
Opp = 16, Adj = 30, Hyp = 34 · Right Triangle → sin(θ)
8. 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)
9. 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)
10. In a right-angled triangle, the side opposite angle θ is 20 cm, the adjacent side is 48 cm, and the hypotenuse is 52 cm. Write cos(θ) as a simplified fraction.
Opp = 20, Adj = 48, Hyp = 52 · 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 sin(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → sin(θ)
12. 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 sin(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → sin(θ)
12 questions · Seed 60 · 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 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 28/100, which simplifies by dividing by 4 to 7/25.
2. 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.
3. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 24/26, which simplifies by dividing by 2 to 12/13.
4. 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.
5. 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.
6. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 105/119, which simplifies by dividing by 7 to 15/17.
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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 16/34, which simplifies by dividing by 2 to 8/17.
8. 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.
9. 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.
10. In a right-angled triangle, the side opposite angle θ is 20 cm, the adjacent side is 48 cm, and the hypotenuse is 52 cm. Write cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 48/52, which simplifies by dividing by 4 to 12/13.
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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 49/175, which simplifies by dividing by 7 to 7/25.
12. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 9/15, which simplifies by dividing by 3 to 3/5.
12 questions · Seed 60 · Age guidance, not curriculum certification