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 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)
2. 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 cos(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · 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 16 cm, the adjacent side is 30 cm, and the hypotenuse is 34 cm. Write sin(θ) as a simplified fraction.
Opp = 16, Adj = 30, Hyp = 34 · Right Triangle → sin(θ)
5. 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)
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 sin(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · Right Triangle → sin(θ)
7. 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 cos(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → cos(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 tan(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → tan(θ)
9. 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)
10. 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)
11. 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 tan(θ) as a simplified fraction.
Opp = 20, Adj = 48, Hyp = 52 · Right Triangle → tan(θ)
12. 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 sin(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → sin(θ)
12 questions · Seed 104744 · 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 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.
2. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 60/68, which simplifies by dividing by 4 to 15/17.
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 16 cm, the adjacent side is 30 cm, and the hypotenuse is 34 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 16/34, which simplifies by dividing by 2 to 8/17.
5. 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.
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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 32/68, which simplifies by dividing by 4 to 8/17.
7. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 90/102, which simplifies by dividing by 6 to 15/17.
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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 10/24, which simplifies by dividing by 2 to 5/12.
9. 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.
10. 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.
11. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 20/48, which simplifies by dividing by 4 to 5/12.
12. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 5/13, which simplifies by dividing by 1 to 5/13.
12 questions · Seed 104744 · 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 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)
2. 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 cos(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · 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 16 cm, the adjacent side is 30 cm, and the hypotenuse is 34 cm. Write sin(θ) as a simplified fraction.
Opp = 16, Adj = 30, Hyp = 34 · Right Triangle → sin(θ)
5. 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)
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 sin(θ) as a simplified fraction.
Opp = 32, Adj = 60, Hyp = 68 · Right Triangle → sin(θ)
7. 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 cos(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → cos(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 tan(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → tan(θ)
9. 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)
10. 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)
11. 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 tan(θ) as a simplified fraction.
Opp = 20, Adj = 48, Hyp = 52 · Right Triangle → tan(θ)
12. 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 sin(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → sin(θ)
12 questions · Seed 104744 · 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 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.
2. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 60/68, which simplifies by dividing by 4 to 15/17.
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 16 cm, the adjacent side is 30 cm, and the hypotenuse is 34 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 16/34, which simplifies by dividing by 2 to 8/17.
5. 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.
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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 32/68, which simplifies by dividing by 4 to 8/17.
7. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 90/102, which simplifies by dividing by 6 to 15/17.
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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 10/24, which simplifies by dividing by 2 to 5/12.
9. 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.
10. 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.
11. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 20/48, which simplifies by dividing by 4 to 5/12.
12. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 5/13, which simplifies by dividing by 1 to 5/13.
12 questions · Seed 104744 · Age guidance, not curriculum certification