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 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)
2. 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)
3. 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)
4. 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 sin(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → sin(θ)
5. 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)
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 sin(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · Right Triangle → sin(θ)
7. 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 sin(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → sin(θ)
8. 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 tan(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → tan(θ)
9. 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)
10. 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 tan(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → tan(θ)
11. 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)
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 56 · 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 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.
2. 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.
3. 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.
4. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 42/150, which simplifies by dividing by 6 to 7/25.
5. 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.
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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 56/119, which simplifies by dividing by 7 to 8/17.
7. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 64/136, which simplifies by dividing by 8 to 8/17.
8. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 42/144, which simplifies by dividing by 6 to 7/24.
9. 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.
10. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 5/12, which simplifies by dividing by 1 to 5/12.
11. 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.
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 56 · 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 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)
2. 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)
3. 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)
4. 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 sin(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → sin(θ)
5. 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)
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 sin(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · Right Triangle → sin(θ)
7. 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 sin(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → sin(θ)
8. 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 tan(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → tan(θ)
9. 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)
10. 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 tan(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → tan(θ)
11. 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)
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 56 · 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 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.
2. 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.
3. 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.
4. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 42/150, which simplifies by dividing by 6 to 7/25.
5. 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.
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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 56/119, which simplifies by dividing by 7 to 8/17.
7. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 64/136, which simplifies by dividing by 8 to 8/17.
8. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 42/144, which simplifies by dividing by 6 to 7/24.
9. 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.
10. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 5/12, which simplifies by dividing by 1 to 5/12.
11. 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.
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 56 · Age guidance, not curriculum certification