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 16-18
Right-triangle trigonometry (SOHCAHTOA)
Take your time. Show your thinking.
1. 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)
2. 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)
3. 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 sin(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → sin(θ)
4. 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 cos(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → cos(θ)
5. 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 sin(θ) as a simplified fraction.
Opp = 21, Adj = 72, Hyp = 75 · Right Triangle → sin(θ)
6. 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 cos(θ) as a simplified fraction.
Opp = 16, Adj = 30, Hyp = 34 · Right Triangle → cos(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 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)
9. 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)
10. 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 sin(θ) as a simplified fraction.
Opp = 15, Adj = 20, Hyp = 25 · Right Triangle → sin(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 cos(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → cos(θ)
12. 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)
12 questions · Seed 59 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18
Right-triangle trigonometry (SOHCAHTOA)
Answers and reasoning. Review before teaching.
1. 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.
2. 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.
3. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 3/5, which simplifies by dividing by 1 to 3/5.
4. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 72/78, which simplifies by dividing by 6 to 12/13.
5. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 21/75, which simplifies by dividing by 3 to 7/25.
6. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 30/34, which simplifies by dividing by 2 to 15/17.
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 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.
9. 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.
10. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 15/25, which simplifies by dividing by 5 to 3/5.
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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 36/39, which simplifies by dividing by 3 to 12/13.
12. 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.
12 questions · Seed 59 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18
Right-triangle trigonometry (SOHCAHTOA)
Take your time. Show your thinking.
1. 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)
2. 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)
3. 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 sin(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → sin(θ)
4. 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 cos(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → cos(θ)
5. 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 sin(θ) as a simplified fraction.
Opp = 21, Adj = 72, Hyp = 75 · Right Triangle → sin(θ)
6. 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 cos(θ) as a simplified fraction.
Opp = 16, Adj = 30, Hyp = 34 · Right Triangle → cos(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 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)
9. 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)
10. 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 sin(θ) as a simplified fraction.
Opp = 15, Adj = 20, Hyp = 25 · Right Triangle → sin(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 cos(θ) as a simplified fraction.
Opp = 15, Adj = 36, Hyp = 39 · Right Triangle → cos(θ)
12. 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)
12 questions · Seed 59 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18
Right-triangle trigonometry (SOHCAHTOA)
Answers and reasoning. Review before teaching.
1. 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.
2. 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.
3. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 3/5, which simplifies by dividing by 1 to 3/5.
4. 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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 72/78, which simplifies by dividing by 6 to 12/13.
5. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 21/75, which simplifies by dividing by 3 to 7/25.
6. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 30/34, which simplifies by dividing by 2 to 15/17.
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 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.
9. 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.
10. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 15/25, which simplifies by dividing by 5 to 3/5.
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 cos(θ) as a simplified fraction.
12/13
cos(θ) = adjacent ÷ hypotenuse = 36/39, which simplifies by dividing by 3 to 12/13.
12. 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.
12 questions · Seed 59 · Age guidance, not curriculum certification