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 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write sin(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → sin(θ)
2. 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)
3. 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 sin(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → sin(θ)
4. 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 cos(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → cos(θ)
5. 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 tan(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → tan(θ)
6. 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)
7. 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 sin(θ) as a simplified fraction.
Opp = 35, Adj = 84, Hyp = 91 · Right Triangle → sin(θ)
8. 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 tan(θ) as a simplified fraction.
Opp = 14, Adj = 48, Hyp = 50 · Right Triangle → tan(θ)
9. 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 sin(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → sin(θ)
10. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → tan(θ)
11. 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)
12. 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 questions · Seed 104739 · 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 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 5/13, which simplifies by dividing by 1 to 5/13.
2. 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.
3. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 6/10, which simplifies by dividing by 2 to 3/5.
4. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 15/17, which simplifies by dividing by 1 to 15/17.
5. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 30/72, which simplifies by dividing by 6 to 5/12.
6. 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.
7. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 35/91, which simplifies by dividing by 7 to 5/13.
8. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 14/48, which simplifies by dividing by 2 to 7/24.
9. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 49/175, which simplifies by dividing by 7 to 7/25.
10. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 48/90, which simplifies by dividing by 6 to 8/15.
11. 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.
12. 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 questions · Seed 104739 · 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 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write sin(θ) as a simplified fraction.
Opp = 5, Adj = 12, Hyp = 13 · Right Triangle → sin(θ)
2. 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)
3. 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 sin(θ) as a simplified fraction.
Opp = 6, Adj = 8, Hyp = 10 · Right Triangle → sin(θ)
4. 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 cos(θ) as a simplified fraction.
Opp = 8, Adj = 15, Hyp = 17 · Right Triangle → cos(θ)
5. 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 tan(θ) as a simplified fraction.
Opp = 30, Adj = 72, Hyp = 78 · Right Triangle → tan(θ)
6. 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)
7. 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 sin(θ) as a simplified fraction.
Opp = 35, Adj = 84, Hyp = 91 · Right Triangle → sin(θ)
8. 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 tan(θ) as a simplified fraction.
Opp = 14, Adj = 48, Hyp = 50 · Right Triangle → tan(θ)
9. 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 sin(θ) as a simplified fraction.
Opp = 49, Adj = 168, Hyp = 175 · Right Triangle → sin(θ)
10. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
Opp = 48, Adj = 90, Hyp = 102 · Right Triangle → tan(θ)
11. 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)
12. 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 questions · Seed 104739 · 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 5 cm, the adjacent side is 12 cm, and the hypotenuse is 13 cm. Write sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 5/13, which simplifies by dividing by 1 to 5/13.
2. 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.
3. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 6/10, which simplifies by dividing by 2 to 3/5.
4. 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 cos(θ) as a simplified fraction.
15/17
cos(θ) = adjacent ÷ hypotenuse = 15/17, which simplifies by dividing by 1 to 15/17.
5. 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 tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 30/72, which simplifies by dividing by 6 to 5/12.
6. 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.
7. 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 sin(θ) as a simplified fraction.
5/13
sin(θ) = opposite ÷ hypotenuse = 35/91, which simplifies by dividing by 7 to 5/13.
8. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 14/48, which simplifies by dividing by 2 to 7/24.
9. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 49/175, which simplifies by dividing by 7 to 7/25.
10. In a right-angled triangle, the side opposite angle θ is 48 cm, the adjacent side is 90 cm, and the hypotenuse is 102 cm. Write tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 48/90, which simplifies by dividing by 6 to 8/15.
11. 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.
12. 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 questions · Seed 104739 · Age guidance, not curriculum certification