Trigonometry Worksheets - Free Printable
Educational worksheet: Trigonometry Worksheets. Download and print for classroom or home learning activities.
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Show Answer Key & Explanations
Step-by-step solution for: Trigonometry Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Trigonometry Worksheets
Let’s go through each triangle one by one. For angle a, we need to find:
- Opposite side → the side *across* from angle a (not touching it, except at the vertex)
- Adjacent side → the side *next to* angle a that is NOT the hypotenuse
- Hypotenuse → the longest side, always opposite the right angle
We’ll list them in order: Opposite, Adjacent, Hypotenuse
---
1) Right angle at bottom left. Angle a is at bottom right.
- Opposite = 4 (across from a)
- Adjacent = 5 (next to a, not hypotenuse)
- Hypotenuse = 6.4 (longest side)
→ 4, 5, 6.4
---
2) Right angle at bottom right. Angle a is at top left.
- Opposite = 3 (across from a)
- Adjacent = 8 (next to a, not hypotenuse)
- Hypotenuse = 8.5
→ 3, 8, 8.5
---
3) Right angle at top left. Angle a is at top right.
- Opposite = 9 (across from a — vertical side)
- Adjacent = 4 (horizontal side next to a)
- Hypotenuse = 9.8
→ 9, 4, 9.8
---
4) Right angle at top. Angle a is at top left.
- Opposite = 7 (vertical side across from a)
- Adjacent = 3 (horizontal side next to a)
- Hypotenuse = 7.6
→ 7, 3, 7.6
---
5) Right angle at top right. Angle a is at bottom right.
- Opposite = 5 (top horizontal side — across from a)
- Adjacent = 6 (vertical side next to a)
- Hypotenuse = 7.8
→ 5, 6, 7.8
---
6) Right angle at top left. Angle a is at bottom left.
- Opposite = 6 (top horizontal side — across from a)
- Adjacent = 9 (vertical side next to a)
- Hypotenuse = 10.8
→ 6, 9, 10.8
---
7) Right angle at bottom left. Angle a is at top left.
- Opposite = 9 (bottom horizontal side — across from a)
- Adjacent = 4 (vertical side next to a)
- Hypotenuse = 9.8
→ 9, 4, 9.8
---
8) Right angle at bottom right. Angle a is at top right.
- Opposite = 5 (bottom horizontal side — across from a)
- Adjacent = 3 (vertical side next to a)
- Hypotenuse = 5.8
→ 5, 3, 5.8
---
9) Right angle at bottom left. Angle a is at bottom right.
- Opposite = 5 (left vertical side — across from a)
- Adjacent = 9 (bottom horizontal side next to a)
- Hypotenuse = 10.3
→ 5, 9, 10.3
---
10) Right angle at bottom right. Angle a is at bottom left.
- Opposite = 6 (right vertical side — across from a)
- Adjacent = 5 (bottom horizontal side next to a)
- Hypotenuse = 7.8
→ 6, 5, 7.8
---
11) Same as #1! Right angle at bottom left. Angle a at bottom right.
- Opposite = 4
- Adjacent = 5
- Hypotenuse = 6.4
→ 4, 5, 6.4
---
12) Right angle at top right. Angle a is at top left.
- Opposite = 3 (right vertical side — across from a)
- Adjacent = 6 (top horizontal side next to a)
- Hypotenuse = 6.7
→ 3, 6, 6.7
---
13) Right angle at top right. Angle a is at bottom right.
- Opposite = 8 (top horizontal side — across from a)
- Adjacent = 5 (right vertical side next to a)
- Hypotenuse = 9.4
→ 8, 5, 9.4
---
14) Right angle at bottom left. Angle a is at top left.
- Opposite = 7 (top horizontal side — across from a)
- Adjacent = 3 (left vertical side next to a)
- Hypotenuse = 7.6
→ 7, 3, 7.6
---
15) Right angle at bottom left. Angle a is at top left.
- Opposite = 7 (bottom horizontal side — across from a)
- Adjacent = 3 (left vertical side next to a)
- Hypotenuse = 7.6
→ 7, 3, 7.6
---
Final Answer:
1. 4, 5, 6.4
2. 3, 8, 8.5
3. 9, 4, 9.8
4. 7, 3, 7.6
5. 5, 6, 7.8
6. 6, 9, 10.8
7. 9, 4, 9.8
8. 5, 3, 5.8
9. 5, 9, 10.3
10. 6, 5, 7.8
11. 4, 5, 6.4
12. 3, 6, 6.7
13. 8, 5, 9.4
14. 7, 3, 7.6
15. 7, 3, 7.6
- Opposite side → the side *across* from angle a (not touching it, except at the vertex)
- Adjacent side → the side *next to* angle a that is NOT the hypotenuse
- Hypotenuse → the longest side, always opposite the right angle
We’ll list them in order: Opposite, Adjacent, Hypotenuse
---
1) Right angle at bottom left. Angle a is at bottom right.
- Opposite = 4 (across from a)
- Adjacent = 5 (next to a, not hypotenuse)
- Hypotenuse = 6.4 (longest side)
→ 4, 5, 6.4
---
2) Right angle at bottom right. Angle a is at top left.
- Opposite = 3 (across from a)
- Adjacent = 8 (next to a, not hypotenuse)
- Hypotenuse = 8.5
→ 3, 8, 8.5
---
3) Right angle at top left. Angle a is at top right.
- Opposite = 9 (across from a — vertical side)
- Adjacent = 4 (horizontal side next to a)
- Hypotenuse = 9.8
→ 9, 4, 9.8
---
4) Right angle at top. Angle a is at top left.
- Opposite = 7 (vertical side across from a)
- Adjacent = 3 (horizontal side next to a)
- Hypotenuse = 7.6
→ 7, 3, 7.6
---
5) Right angle at top right. Angle a is at bottom right.
- Opposite = 5 (top horizontal side — across from a)
- Adjacent = 6 (vertical side next to a)
- Hypotenuse = 7.8
→ 5, 6, 7.8
---
6) Right angle at top left. Angle a is at bottom left.
- Opposite = 6 (top horizontal side — across from a)
- Adjacent = 9 (vertical side next to a)
- Hypotenuse = 10.8
→ 6, 9, 10.8
---
7) Right angle at bottom left. Angle a is at top left.
- Opposite = 9 (bottom horizontal side — across from a)
- Adjacent = 4 (vertical side next to a)
- Hypotenuse = 9.8
→ 9, 4, 9.8
---
8) Right angle at bottom right. Angle a is at top right.
- Opposite = 5 (bottom horizontal side — across from a)
- Adjacent = 3 (vertical side next to a)
- Hypotenuse = 5.8
→ 5, 3, 5.8
---
9) Right angle at bottom left. Angle a is at bottom right.
- Opposite = 5 (left vertical side — across from a)
- Adjacent = 9 (bottom horizontal side next to a)
- Hypotenuse = 10.3
→ 5, 9, 10.3
---
10) Right angle at bottom right. Angle a is at bottom left.
- Opposite = 6 (right vertical side — across from a)
- Adjacent = 5 (bottom horizontal side next to a)
- Hypotenuse = 7.8
→ 6, 5, 7.8
---
11) Same as #1! Right angle at bottom left. Angle a at bottom right.
- Opposite = 4
- Adjacent = 5
- Hypotenuse = 6.4
→ 4, 5, 6.4
---
12) Right angle at top right. Angle a is at top left.
- Opposite = 3 (right vertical side — across from a)
- Adjacent = 6 (top horizontal side next to a)
- Hypotenuse = 6.7
→ 3, 6, 6.7
---
13) Right angle at top right. Angle a is at bottom right.
- Opposite = 8 (top horizontal side — across from a)
- Adjacent = 5 (right vertical side next to a)
- Hypotenuse = 9.4
→ 8, 5, 9.4
---
14) Right angle at bottom left. Angle a is at top left.
- Opposite = 7 (top horizontal side — across from a)
- Adjacent = 3 (left vertical side next to a)
- Hypotenuse = 7.6
→ 7, 3, 7.6
---
15) Right angle at bottom left. Angle a is at top left.
- Opposite = 7 (bottom horizontal side — across from a)
- Adjacent = 3 (left vertical side next to a)
- Hypotenuse = 7.6
→ 7, 3, 7.6
---
Final Answer:
1. 4, 5, 6.4
2. 3, 8, 8.5
3. 9, 4, 9.8
4. 7, 3, 7.6
5. 5, 6, 7.8
6. 6, 9, 10.8
7. 9, 4, 9.8
8. 5, 3, 5.8
9. 5, 9, 10.3
10. 6, 5, 7.8
11. 4, 5, 6.4
12. 3, 6, 6.7
13. 8, 5, 9.4
14. 7, 3, 7.6
15. 7, 3, 7.6
Parent Tip: Review the logic above to help your child master the concept of geometry sin cos tan worksheet.
