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 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write sin(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → sin(θ)
2. 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)
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 sin(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → sin(θ)
4. 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)
5. 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 cos(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → cos(θ)
6. 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 tan(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → tan(θ)
7. 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)
8. 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)
9. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → tan(θ)
10. In a right-angled triangle, the side opposite angle θ is 25 cm, the adjacent side is 60 cm, and the hypotenuse is 65 cm. Write tan(θ) as a simplified fraction.
Opp = 25, Adj = 60, Hyp = 65 · Right Triangle → tan(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 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write cos(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → cos(θ)
12 questions · Seed 104735 · 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 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 24/40, which simplifies by dividing by 8 to 3/5.
2. 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.
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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 6/10, which simplifies by dividing by 2 to 3/5.
4. 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.
5. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 12/13, which simplifies by dividing by 1 to 12/13.
6. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 30/72, which simplifies by dividing by 6 to 5/12.
7. 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.
8. 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.
9. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 48/90, which simplifies by dividing by 6 to 8/15.
10. In a right-angled triangle, the side opposite angle θ is 25 cm, the adjacent side is 60 cm, and the hypotenuse is 65 cm. Write tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 25/60, which simplifies by dividing by 5 to 5/12.
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 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 32/40, which simplifies by dividing by 8 to 4/5.
12 questions · Seed 104735 · 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 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write sin(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → sin(θ)
2. 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)
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 sin(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → sin(θ)
4. 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)
5. 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 cos(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → cos(θ)
6. 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 tan(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → tan(θ)
7. 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)
8. 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)
9. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → tan(θ)
10. In a right-angled triangle, the side opposite angle θ is 25 cm, the adjacent side is 60 cm, and the hypotenuse is 65 cm. Write tan(θ) as a simplified fraction.
Opp = 25, Adj = 60, Hyp = 65 · Right Triangle → tan(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 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write cos(θ) as a simplified fraction.
Opp = 24, Adj = 32, Hyp = 40 · Right Triangle → cos(θ)
12 questions · Seed 104735 · 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 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 24/40, which simplifies by dividing by 8 to 3/5.
2. 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.
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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 6/10, which simplifies by dividing by 2 to 3/5.
4. 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.
5. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 12/13, which simplifies by dividing by 1 to 12/13.
6. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 30/72, which simplifies by dividing by 6 to 5/12.
7. 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.
8. 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.
9. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 48/90, which simplifies by dividing by 6 to 8/15.
10. In a right-angled triangle, the side opposite angle θ is 25 cm, the adjacent side is 60 cm, and the hypotenuse is 65 cm. Write tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 25/60, which simplifies by dividing by 5 to 5/12.
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 24 cm, the adjacent side is 32 cm, and the hypotenuse is 40 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 32/40, which simplifies by dividing by 8 to 4/5.
12 questions · Seed 104735 · Age guidance, not curriculum certification