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 8 cm, the adjacent side is 15 cm, and the hypotenuse is 17 cm. Write tan(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → tan(θ)
2. 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 tan(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → tan(θ)
3. 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)
4. 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)
5. 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)
6. 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)
7. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write cos(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → cos(θ)
8. 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 cos(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → cos(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 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 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)
12. 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 cos(θ) as a simplified fraction.
Opp = 24, Adj = 45, Hyp = 51 · Right Triangle → cos(θ)
12 questions · Seed 45 · 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 8 cm, the adjacent side is 15 cm, and the hypotenuse is 17 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 8/15, which simplifies by dividing by 1 to 8/15.
2. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 15/36, which simplifies by dividing by 3 to 5/12.
3. 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.
4. 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.
5. 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.
6. 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.
7. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 192/200, which simplifies by dividing by 8 to 24/25.
8. 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 cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 168/175, which simplifies by dividing by 7 to 24/25.
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 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 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.
12. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 45/51, which simplifies by dividing by 3 to 15/17.
12 questions · Seed 45 · 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 8 cm, the adjacent side is 15 cm, and the hypotenuse is 17 cm. Write tan(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → tan(θ)
2. 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 tan(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → tan(θ)
3. 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)
4. 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)
5. 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)
6. 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)
7. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write cos(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → cos(θ)
8. 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 cos(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → cos(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 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 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)
12. 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 cos(θ) as a simplified fraction.
Opp = 24, Adj = 45, Hyp = 51 · Right Triangle → cos(θ)
12 questions · Seed 45 · 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 8 cm, the adjacent side is 15 cm, and the hypotenuse is 17 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 8/15, which simplifies by dividing by 1 to 8/15.
2. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 15/36, which simplifies by dividing by 3 to 5/12.
3. 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.
4. 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.
5. 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.
6. 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.
7. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 192 cm, and the hypotenuse is 200 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 192/200, which simplifies by dividing by 8 to 24/25.
8. 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 cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 168/175, which simplifies by dividing by 7 to 24/25.
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 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 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.
12. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 45/51, which simplifies by dividing by 3 to 15/17.
12 questions · Seed 45 · Age guidance, not curriculum certification