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 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write tan(θ) as a simplified fraction.
Opp = 21, Adj = 72, Hyp = 75 · Right Triangle → tan(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 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write tan(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → tan(θ)
5. In a right-angled triangle, the side opposite angle θ is 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write cos(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → cos(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 sin(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → sin(θ)
7. 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)
8. 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 sin(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → sin(θ)
9. 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)
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 cos(θ) as a simplified fraction.
Opp = 25, Adj = 60, Hyp = 65 · Right Triangle → cos(θ)
11. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write sin(θ) as a simplified fraction.
Opp = 40, Adj = 96, Hyp = 104 · Right Triangle → sin(θ)
12. 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 tan(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → tan(θ)
12 questions · Seed 43 · 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 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 21/72, which simplifies by dividing by 3 to 7/24.
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 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 12/16, which simplifies by dividing by 4 to 3/4.
5. In a right-angled triangle, the side opposite angle θ is 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 16/20, which simplifies by dividing by 4 to 4/5.
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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 21/35, which simplifies by dividing by 7 to 3/5.
7. 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.
8. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 10/26, which simplifies by dividing by 2 to 5/13.
9. 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.
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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 60/65, which simplifies by dividing by 5 to 12/13.
11. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 40/104, which simplifies by dividing by 8 to 5/13.
12. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 28/96, which simplifies by dividing by 4 to 7/24.
12 questions · Seed 43 · 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 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write tan(θ) as a simplified fraction.
Opp = 21, Adj = 72, Hyp = 75 · Right Triangle → tan(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 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write tan(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → tan(θ)
5. In a right-angled triangle, the side opposite angle θ is 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write cos(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → cos(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 sin(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → sin(θ)
7. 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)
8. 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 sin(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → sin(θ)
9. 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)
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 cos(θ) as a simplified fraction.
Opp = 25, Adj = 60, Hyp = 65 · Right Triangle → cos(θ)
11. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write sin(θ) as a simplified fraction.
Opp = 40, Adj = 96, Hyp = 104 · Right Triangle → sin(θ)
12. 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 tan(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → tan(θ)
12 questions · Seed 43 · 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 21 cm, the adjacent side is 72 cm, and the hypotenuse is 75 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 21/72, which simplifies by dividing by 3 to 7/24.
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 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 12/16, which simplifies by dividing by 4 to 3/4.
5. In a right-angled triangle, the side opposite angle θ is 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 16/20, which simplifies by dividing by 4 to 4/5.
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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 21/35, which simplifies by dividing by 7 to 3/5.
7. 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.
8. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 10/26, which simplifies by dividing by 2 to 5/13.
9. 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.
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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 60/65, which simplifies by dividing by 5 to 12/13.
11. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 40/104, which simplifies by dividing by 8 to 5/13.
12. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 28/96, which simplifies by dividing by 4 to 7/24.
12 questions · Seed 43 · Age guidance, not curriculum certification