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 13-15
Right-triangle trigonometry (SOHCAHTOA)
Take your time. Show your thinking.
1. 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)
2. 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)
3. 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)
4. 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 tan(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → tan(θ)
5. 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 sin(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → sin(θ)
6. In a right-angled triangle, the side opposite angle θ is 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write sin(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → sin(θ)
7. 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)
8. 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 cos(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → cos(θ)
9. 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)
10. 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)
11. 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)
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 tan(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → tan(θ)
12 questions · Seed 104733 · 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 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.
2. 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.
3. 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.
4. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 49/168, which simplifies by dividing by 7 to 7/24.
5. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 8/17, which simplifies by dividing by 1 to 8/17.
6. In a right-angled triangle, the side opposite angle θ is 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 28/100, which simplifies by dividing by 4 to 7/25.
7. 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.
8. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 28/35, which simplifies by dividing by 7 to 4/5.
9. 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.
10. 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.
11. 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.
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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 5/12, which simplifies by dividing by 1 to 5/12.
12 questions · Seed 104733 · 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 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)
2. 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)
3. 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)
4. 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 tan(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → tan(θ)
5. 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 sin(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → sin(θ)
6. In a right-angled triangle, the side opposite angle θ is 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write sin(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → sin(θ)
7. 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)
8. 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 cos(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → cos(θ)
9. 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)
10. 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)
11. 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)
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 tan(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → tan(θ)
12 questions · Seed 104733 · 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 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.
2. 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.
3. 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.
4. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 49/168, which simplifies by dividing by 7 to 7/24.
5. 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 sin(θ) as a simplified fraction.
8/17
sin(θ) = opposite ÷ hypotenuse = 8/17, which simplifies by dividing by 1 to 8/17.
6. In a right-angled triangle, the side opposite angle θ is 28 cm, the adjacent side is 96 cm, and the hypotenuse is 100 cm. Write sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 28/100, which simplifies by dividing by 4 to 7/25.
7. 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.
8. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 28/35, which simplifies by dividing by 7 to 4/5.
9. 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.
10. 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.
11. 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.
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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 5/12, which simplifies by dividing by 1 to 5/12.
12 questions · Seed 104733 · Age guidance, not curriculum certification