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 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)
2. 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)
3. In a right-angled triangle, the side opposite angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm. Write sin(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → sin(θ)
4. 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 sin(θ) as a simplified fraction.
Opp = 20, Adj = 48, Hyp = 52 · Right Triangle → sin(θ)
5. 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)
6. 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 tan(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · Right Triangle → tan(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 cos(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → cos(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 sin(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → sin(θ)
9. 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)
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 tan(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → tan(θ)
11. 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 cos(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → cos(θ)
12. 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 cos(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → cos(θ)
12 questions · Seed 52 · 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 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.
2. 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.
3. In a right-angled triangle, the side opposite angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 3/5, which simplifies by dividing by 1 to 3/5.
4. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 20/52, which simplifies by dividing by 4 to 5/13.
5. 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.
6. 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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 32/60, which simplifies by dividing by 4 to 8/15.
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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 120/136, which simplifies by dividing by 8 to 15/17.
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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 42/150, which simplifies by dividing by 6 to 7/25.
9. 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.
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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 42/144, which simplifies by dividing by 6 to 7/24.
11. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 24/30, which simplifies by dividing by 6 to 4/5.
12. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 8/10, which simplifies by dividing by 2 to 4/5.
12 questions · Seed 52 · 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 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)
2. 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)
3. In a right-angled triangle, the side opposite angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm. Write sin(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → sin(θ)
4. 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 sin(θ) as a simplified fraction.
Opp = 20, Adj = 48, Hyp = 52 · Right Triangle → sin(θ)
5. 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)
6. 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 tan(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · Right Triangle → tan(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 cos(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → cos(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 sin(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → sin(θ)
9. 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)
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 tan(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → tan(θ)
11. 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 cos(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → cos(θ)
12. 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 cos(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → cos(θ)
12 questions · Seed 52 · 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 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.
2. 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.
3. In a right-angled triangle, the side opposite angle θ is 3 cm, the adjacent side is 4 cm, and the hypotenuse is 5 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 3/5, which simplifies by dividing by 1 to 3/5.
4. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 20/52, which simplifies by dividing by 4 to 5/13.
5. 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.
6. 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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 32/60, which simplifies by dividing by 4 to 8/15.
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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 120/136, which simplifies by dividing by 8 to 15/17.
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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 42/150, which simplifies by dividing by 6 to 7/25.
9. 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.
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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 42/144, which simplifies by dividing by 6 to 7/24.
11. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 24/30, which simplifies by dividing by 6 to 4/5.
12. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 8/10, which simplifies by dividing by 2 to 4/5.
12 questions · Seed 52 · Age guidance, not curriculum certification