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 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)
2. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write cos(θ) as a simplified fraction.
Opp = 21, Adj = 72, Hyp = 75 · Right Triangle → cos(θ)
3. 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)
4. 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 cos(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → cos(θ)
5. In a right-angled triangle, the side opposite angle θ is 14 cm, the adjacent side is 48 cm, and the hypotenuse is 50 cm. Write sin(θ) as a simplified fraction.
Opp = 14, Adj = 48, Hyp = 50 · Right Triangle → sin(θ)
6. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 28 cm, and the hypotenuse is 35 cm. Write cos(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → cos(θ)
7. 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 cos(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → cos(θ)
8. 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 sin(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → sin(θ)
9. 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)
10. 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)
11. 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)
12. 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)
12 questions · Seed 48 · 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 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.
2. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 72/75, which simplifies by dividing by 3 to 24/25.
3. 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.
4. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 12/15, which simplifies by dividing by 3 to 4/5.
5. In a right-angled triangle, the side opposite angle θ is 14 cm, the adjacent side is 48 cm, and the hypotenuse is 50 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 14/50, which simplifies by dividing by 2 to 7/25.
6. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 28 cm, and the hypotenuse is 35 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 28/35, which simplifies by dividing by 7 to 4/5.
7. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 72/78, which simplifies by dividing by 6 to 12/13.
8. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 56/200, which simplifies by dividing by 8 to 7/25.
9. 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.
10. 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.
11. 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.
12. 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.
12 questions · Seed 48 · 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 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)
2. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write cos(θ) as a simplified fraction.
Opp = 21, Adj = 72, Hyp = 75 · Right Triangle → cos(θ)
3. 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)
4. 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 cos(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → cos(θ)
5. In a right-angled triangle, the side opposite angle θ is 14 cm, the adjacent side is 48 cm, and the hypotenuse is 50 cm. Write sin(θ) as a simplified fraction.
Opp = 14, Adj = 48, Hyp = 50 · Right Triangle → sin(θ)
6. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 28 cm, and the hypotenuse is 35 cm. Write cos(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → cos(θ)
7. 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 cos(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → cos(θ)
8. 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 sin(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → sin(θ)
9. 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)
10. 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)
11. 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)
12. 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)
12 questions · Seed 48 · 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 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.
2. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 72/75, which simplifies by dividing by 3 to 24/25.
3. 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.
4. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 12/15, which simplifies by dividing by 3 to 4/5.
5. In a right-angled triangle, the side opposite angle θ is 14 cm, the adjacent side is 48 cm, and the hypotenuse is 50 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 14/50, which simplifies by dividing by 2 to 7/25.
6. In a right-angled triangle, the side opposite angle θ is 21 cm, the adjacent side is 28 cm, and the hypotenuse is 35 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 28/35, which simplifies by dividing by 7 to 4/5.
7. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 72/78, which simplifies by dividing by 6 to 12/13.
8. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 56/200, which simplifies by dividing by 8 to 7/25.
9. 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.
10. 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.
11. 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.
12. 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.
12 questions · Seed 48 · Age guidance, not curriculum certification