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 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write cos(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → cos(θ)
2. 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)
3. 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 sin(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → sin(θ)
4. 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 cos(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → cos(θ)
5. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 20 cm, and the hypotenuse is 25 cm. Write cos(θ) as a simplified fraction.
Opp = 15, Adj = 20, Hyp = 25 · Right Triangle → cos(θ)
6. 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 sin(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → sin(θ)
7. 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)
8. 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 tan(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → tan(θ)
9. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 120 cm, and the hypotenuse is 125 cm. Write sin(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · 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 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 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)
12. 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)
12 questions · Seed 104740 · 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 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 75/85, which simplifies by dividing by 5 to 15/17.
2. 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.
3. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 15/39, which simplifies by dividing by 3 to 5/13.
4. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 4/5, which simplifies by dividing by 1 to 4/5.
5. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 20 cm, and the hypotenuse is 25 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 20/25, which simplifies by dividing by 5 to 4/5.
6. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 12/20, which simplifies by dividing by 4 to 3/5.
7. 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.
8. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 9/12, which simplifies by dividing by 3 to 3/4.
9. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 120 cm, and the hypotenuse is 125 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 35/125, which simplifies by dividing by 5 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 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 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.
12. 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.
12 questions · Seed 104740 · 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 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write cos(θ) as a simplified fraction.
Opp = 40, Adj = 75, Hyp = 85 · Right Triangle → cos(θ)
2. 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)
3. 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 sin(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → sin(θ)
4. 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 cos(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → cos(θ)
5. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 20 cm, and the hypotenuse is 25 cm. Write cos(θ) as a simplified fraction.
Opp = 15, Adj = 20, Hyp = 25 · Right Triangle → cos(θ)
6. 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 sin(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → sin(θ)
7. 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)
8. 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 tan(θ) as a simplified fraction.
Opp = 9, Adj = 12, Hyp = 15 · Right Triangle → tan(θ)
9. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 120 cm, and the hypotenuse is 125 cm. Write sin(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · 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 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 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)
12. 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)
12 questions · Seed 104740 · 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 40 cm, the adjacent side is 75 cm, and the hypotenuse is 85 cm. Write cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 75/85, which simplifies by dividing by 5 to 15/17.
2. 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.
3. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 15/39, which simplifies by dividing by 3 to 5/13.
4. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 4/5, which simplifies by dividing by 1 to 4/5.
5. In a right-angled triangle, the side opposite angle θ is 15 cm, the adjacent side is 20 cm, and the hypotenuse is 25 cm. Write cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 20/25, which simplifies by dividing by 5 to 4/5.
6. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 12/20, which simplifies by dividing by 4 to 3/5.
7. 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.
8. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 9/12, which simplifies by dividing by 3 to 3/4.
9. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 120 cm, and the hypotenuse is 125 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 35/125, which simplifies by dividing by 5 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 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 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.
12. 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.
12 questions · Seed 104740 · Age guidance, not curriculum certification