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 tan(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → tan(θ)
2. 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)
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 sin(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → sin(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 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)
6. 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 tan(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → tan(θ)
7. 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 tan(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → tan(θ)
8. 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)
9. 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 sin(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → sin(θ)
10. 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 cos(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → cos(θ)
11. 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)
12. 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)
12 questions · Seed 104729 · 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 42/144, which simplifies by dividing by 6 to 7/24.
2. 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.
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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 7/25, which simplifies by dividing by 1 to 7/25.
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 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.
6. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 3/4, which simplifies by dividing by 1 to 3/4.
7. 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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 64/120, which simplifies by dividing by 8 to 8/15.
8. 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.
9. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 18/30, which simplifies by dividing by 6 to 3/5.
10. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 24/30, which simplifies by dividing by 6 to 4/5.
11. 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.
12. 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.
12 questions · Seed 104729 · 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 tan(θ) as a simplified fraction.
Opp = 42, Adj = 144, Hyp = 150 · Right Triangle → tan(θ)
2. 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)
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 sin(θ) as a simplified fraction.
Opp = 7, Adj = 24, Hyp = 25 · Right Triangle → sin(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 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)
6. 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 tan(θ) as a simplified fraction.
Opp = 3, Adj = 4, Hyp = 5 · Right Triangle → tan(θ)
7. 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 tan(θ) as a simplified fraction.
Opp = 64, Adj = 120, Hyp = 136 · Right Triangle → tan(θ)
8. 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)
9. 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 sin(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → sin(θ)
10. 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 cos(θ) as a simplified fraction.
Opp = 18, Adj = 24, Hyp = 30 · Right Triangle → cos(θ)
11. 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)
12. 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)
12 questions · Seed 104729 · 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 tan(θ) as a simplified fraction.
7/24
tan(θ) = opposite ÷ adjacent = 42/144, which simplifies by dividing by 6 to 7/24.
2. 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.
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 sin(θ) as a simplified fraction.
7/25
sin(θ) = opposite ÷ hypotenuse = 7/25, which simplifies by dividing by 1 to 7/25.
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 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.
6. 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 tan(θ) as a simplified fraction.
3/4
tan(θ) = opposite ÷ adjacent = 3/4, which simplifies by dividing by 1 to 3/4.
7. 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 tan(θ) as a simplified fraction.
8/15
tan(θ) = opposite ÷ adjacent = 64/120, which simplifies by dividing by 8 to 8/15.
8. 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.
9. 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 sin(θ) as a simplified fraction.
3/5
sin(θ) = opposite ÷ hypotenuse = 18/30, which simplifies by dividing by 6 to 3/5.
10. 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 cos(θ) as a simplified fraction.
4/5
cos(θ) = adjacent ÷ hypotenuse = 24/30, which simplifies by dividing by 6 to 4/5.
11. 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.
12. 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.
12 questions · Seed 104729 · Age guidance, not curriculum certification