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 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write tan(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → tan(θ)
2. 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)
3. 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)
4. 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 sin(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → sin(θ)
5. 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 sin(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → sin(θ)
6. 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 cos(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → cos(θ)
7. 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 sin(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → sin(θ)
8. 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 cos(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → cos(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 sin(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → sin(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 tan(θ) as a simplified fraction.
Opp = 24, Adj = 45, Hyp = 51 · Right Triangle → tan(θ)
11. 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 cos(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → cos(θ)
12. 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 sin(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → sin(θ)
12 questions · Seed 104743 · 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 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 7/24, which simplifies by dividing by 1 to 7/24.
2. 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.
3. 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.
4. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 10/26, which simplifies by dividing by 2 to 5/13.
5. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 56/200, which simplifies by dividing by 8 to 7/25.
6. 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 cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 120/125, which simplifies by dividing by 5 to 24/25.
7. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 21/35, which simplifies by dividing by 7 to 3/5.
8. 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 cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 96/100, which simplifies by dividing by 4 to 24/25.
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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 3/5, which simplifies by dividing by 1 to 3/5.
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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 24/45, which simplifies by dividing by 3 to 8/15.
11. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 120/136, which simplifies by dividing by 8 to 15/17.
12. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 7/25, which simplifies by dividing by 1 to 7/25.
12 questions · Seed 104743 · 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 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write tan(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → tan(θ)
2. 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)
3. 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)
4. 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 sin(θ) as a simplified fraction.
Opp = 10, Adj = 24, Hyp = 26 · Right Triangle → sin(θ)
5. 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 sin(θ) as a simplified fraction.
Opp = 56, Adj = 192, Hyp = 200 · Right Triangle → sin(θ)
6. 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 cos(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → cos(θ)
7. 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 sin(θ) as a simplified fraction.
Opp = 21, Adj = 28, Hyp = 35 · Right Triangle → sin(θ)
8. 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 cos(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → cos(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 sin(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → sin(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 tan(θ) as a simplified fraction.
Opp = 24, Adj = 45, Hyp = 51 · Right Triangle → tan(θ)
11. 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 cos(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → cos(θ)
12. 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 sin(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → sin(θ)
12 questions · Seed 104743 · 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 7 cm, the adjacent side is 24 cm, and the hypotenuse is 25 cm. Write tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 7/24, which simplifies by dividing by 1 to 7/24.
2. 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.
3. 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.
4. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 10/26, which simplifies by dividing by 2 to 5/13.
5. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 56/200, which simplifies by dividing by 8 to 7/25.
6. 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 cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 120/125, which simplifies by dividing by 5 to 24/25.
7. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 21/35, which simplifies by dividing by 7 to 3/5.
8. 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 cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 96/100, which simplifies by dividing by 4 to 24/25.
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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 3/5, which simplifies by dividing by 1 to 3/5.
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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 24/45, which simplifies by dividing by 3 to 8/15.
11. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 120/136, which simplifies by dividing by 8 to 15/17.
12. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 7/25, which simplifies by dividing by 1 to 7/25.
12 questions · Seed 104743 · Age guidance, not curriculum certification