Apply sine, cosine and tangent ratios (SOHCAHTOA) in right-angled triangles and simplify to lowest terms. Review suitability for your learners before teaching.
Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.
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 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)
2. 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 tan(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → tan(θ)
3. In a right-angled triangle, the side opposite angle θ is 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write cos(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → cos(θ)
4. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 84 cm, and the hypotenuse is 91 cm. Write tan(θ) as a simplified fraction.
Opp = 35, Adj = 84, Hyp = 91 · Right Triangle → tan(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 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)
7. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 105 cm, and the hypotenuse is 119 cm. Write sin(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · Right Triangle → sin(θ)
8. 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 tan(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → tan(θ)
9. 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)
10. 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)
11. 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)
12. In a right-angled triangle, the side opposite angle θ is 64 cm, the adjacent side is 120 cm, and the hypotenuse is 136 cm. Write sin(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → sin(θ)
12 questions · Seed 104734 · 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 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.
2. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 21/28, which simplifies by dividing by 7 to 3/4.
3. In a right-angled triangle, the side opposite angle θ is 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 24/25, which simplifies by dividing by 1 to 24/25.
4. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 84 cm, and the hypotenuse is 91 cm. Write tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 35/84, which simplifies by dividing by 7 to 5/12.
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 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.
7. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 105 cm, and the hypotenuse is 119 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 56/119, which simplifies by dividing by 7 to 8/17.
8. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 35/120, which simplifies by dividing by 5 to 7/24.
9. 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.
10. 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.
11. 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.
12. In a right-angled triangle, the side opposite angle θ is 64 cm, the adjacent side is 120 cm, and the hypotenuse is 136 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 64/136, which simplifies by dividing by 8 to 8/17.
12 questions · Seed 104734 · 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 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)
2. 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 tan(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → tan(θ)
3. In a right-angled triangle, the side opposite angle θ is 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write cos(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → cos(θ)
4. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 84 cm, and the hypotenuse is 91 cm. Write tan(θ) as a simplified fraction.
Opp = 35, Adj = 84, Hyp = 91 · Right Triangle → tan(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 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)
7. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 105 cm, and the hypotenuse is 119 cm. Write sin(θ) as a simplified fraction.
Opp = 56, Adj = 105, Hyp = 119 · Right Triangle → sin(θ)
8. 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 tan(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → tan(θ)
9. 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)
10. 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)
11. 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)
12. In a right-angled triangle, the side opposite angle θ is 64 cm, the adjacent side is 120 cm, and the hypotenuse is 136 cm. Write sin(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → sin(θ)
12 questions · Seed 104734 · 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 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.
2. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 21/28, which simplifies by dividing by 7 to 3/4.
3. In a right-angled triangle, the side opposite angle θ is 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 24/25, which simplifies by dividing by 1 to 24/25.
4. In a right-angled triangle, the side opposite angle θ is 35 cm, the adjacent side is 84 cm, and the hypotenuse is 91 cm. Write tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 35/84, which simplifies by dividing by 7 to 5/12.
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 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.
7. In a right-angled triangle, the side opposite angle θ is 56 cm, the adjacent side is 105 cm, and the hypotenuse is 119 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 56/119, which simplifies by dividing by 7 to 8/17.
8. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 35/120, which simplifies by dividing by 5 to 7/24.
9. 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.
10. 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.
11. 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.
12. In a right-angled triangle, the side opposite angle θ is 64 cm, the adjacent side is 120 cm, and the hypotenuse is 136 cm. Write sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 64/136, which simplifies by dividing by 8 to 8/17.
12 questions · Seed 104734 · Age guidance, not curriculum certification