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 42 cm, the adjacent side is 144 cm, and the hypotenuse is 150 cm. Write cos(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → cos(θ)
2. 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)
3. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write tan(θ) as a simplified fraction.
Opp = 40, Adj = 96, Hyp = 104 · Right Triangle → tan(θ)
4. 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)
5. 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)
6. In a right-angled triangle, the side opposite angle θ is 18 cm, the adjacent side is 24 cm, and the hypotenuse is 30 cm. Write tan(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → tan(θ)
7. 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 cos(θ) as a simplified fraction.
Opp = 15, Adj = 20, Hyp = 25 · Right Triangle → cos(θ)
8. 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)
9. 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)
10. 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 tan(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → tan(θ)
11. 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 sin(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → sin(θ)
12. In a right-angled triangle, the side opposite angle θ is 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write tan(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → tan(θ)
12 questions · Seed 46 · 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 42 cm, the adjacent side is 144 cm, and the hypotenuse is 150 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 144/150, which simplifies by dividing by 6 to 24/25.
2. 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.
3. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 40/96, which simplifies by dividing by 8 to 5/12.
4. 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.
5. 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.
6. In a right-angled triangle, the side opposite angle θ is 18 cm, the adjacent side is 24 cm, and the hypotenuse is 30 cm. Write tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 18/24, which simplifies by dividing by 6 to 3/4.
7. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 20/25, which simplifies by dividing by 5 to 4/5.
8. 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.
9. 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.
10. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 28/96, which simplifies by dividing by 4 to 7/24.
11. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 35/125, which simplifies by dividing by 5 to 7/25.
12. In a right-angled triangle, the side opposite angle θ is 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 12/16, which simplifies by dividing by 4 to 3/4.
12 questions · Seed 46 · 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 42 cm, the adjacent side is 144 cm, and the hypotenuse is 150 cm. Write cos(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → cos(θ)
2. 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)
3. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write tan(θ) as a simplified fraction.
Opp = 40, Adj = 96, Hyp = 104 · Right Triangle → tan(θ)
4. 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)
5. 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)
6. In a right-angled triangle, the side opposite angle θ is 18 cm, the adjacent side is 24 cm, and the hypotenuse is 30 cm. Write tan(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → tan(θ)
7. 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 cos(θ) as a simplified fraction.
Opp = 15, Adj = 20, Hyp = 25 · Right Triangle → cos(θ)
8. 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)
9. 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)
10. 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 tan(θ) as a simplified fraction.
Opp = 28, Adj = 96, Hyp = 100 · Right Triangle → tan(θ)
11. 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 sin(θ) as a simplified fraction.
Opp = 35, Adj = 120, Hyp = 125 · Right Triangle → sin(θ)
12. In a right-angled triangle, the side opposite angle θ is 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write tan(θ) as a simplified fraction.
Opp = 12, Adj = 16, Hyp = 20 · Right Triangle → tan(θ)
12 questions · Seed 46 · 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 42 cm, the adjacent side is 144 cm, and the hypotenuse is 150 cm. Write cos(θ) as a simplified fraction.
24/25
cos(θ) = adjacent ÷ hypotenuse = 144/150, which simplifies by dividing by 6 to 24/25.
2. 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.
3. In a right-angled triangle, the side opposite angle θ is 40 cm, the adjacent side is 96 cm, and the hypotenuse is 104 cm. Write tan(θ) as a simplified fraction.
5/12
tan(θ) = opposite ÷ adjacent = 40/96, which simplifies by dividing by 8 to 5/12.
4. 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.
5. 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.
6. In a right-angled triangle, the side opposite angle θ is 18 cm, the adjacent side is 24 cm, and the hypotenuse is 30 cm. Write tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 18/24, which simplifies by dividing by 6 to 3/4.
7. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 20/25, which simplifies by dividing by 5 to 4/5.
8. 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.
9. 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.
10. 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 28/96, which simplifies by dividing by 4 to 7/24.
11. 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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 35/125, which simplifies by dividing by 5 to 7/25.
12. In a right-angled triangle, the side opposite angle θ is 12 cm, the adjacent side is 16 cm, and the hypotenuse is 20 cm. Write tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 12/16, which simplifies by dividing by 4 to 3/4.
12 questions · Seed 46 · Age guidance, not curriculum certification