Let’s solve each problem one by one. We’ll use the definitions of sine, cosine, and tangent for right triangles:
-
sin(angle) = opposite / hypotenuse
-
cos(angle) = adjacent / hypotenuse
-
tan(angle) = opposite / adjacent
We’ll identify the sides relative to the angle asked in each question.
---
1) tan Z
Triangle XYZ, right-angled at Y.
Angle Z is at vertex Z.
- Opposite side to Z: XY = 21
- Adjacent side to Z: YZ = 28
→ tan Z = opposite/adjacent = 21/28 =
3/4
---
2) cos C
Triangle ABC, right-angled at B.
Angle C is at vertex C.
- Adjacent side to C: BC = 16
- Hypotenuse: AC = 34
→ cos C = adjacent/hypotenuse = 16/34 =
8/17
---
3) sin C
Triangle ABC, right-angled at B.
Angle C is at vertex C.
- Opposite side to C: AB = 28
- Hypotenuse: AC = 35
→ sin C = opposite/hypotenuse = 28/35 =
4/5
---
4) tan X
Triangle XYZ, right-angled at Y.
Angle X is at vertex X.
- Opposite side to X: YZ = 32
- Adjacent side to X: XY = 24
→ tan X = opposite/adjacent = 32/24 =
4/3
---
5) cos A
Triangle ABC, right-angled at B.
Angle A is at vertex A.
- Adjacent side to A: AB = 30
- Hypotenuse: AC = 34
→ cos A = adjacent/hypotenuse = 30/34 =
15/17
---
6) sin A
Triangle ABC, right-angled at B.
Angle A is at vertex A.
- Opposite side to A: BC = 32
- Hypotenuse: AC = 40
→ sin A = opposite/hypotenuse = 32/40 =
4/5
---
7) sin Z
Triangle XYZ, right-angled at Y.
Angle Z is at vertex Z.
- Opposite side to Z: XY = 24
- Hypotenuse: XZ = 40
→ sin Z = opposite/hypotenuse = 24/40 =
3/5
---
8) sin C
Triangle ABC, right-angled at B.
Angle C is at vertex C.
- Opposite side to C: AB = 14
- Hypotenuse: AC = 50
→ sin C = opposite/hypotenuse = 14/50 =
7/25
---
9) cos Z
Triangle XYZ, right-angled at Y.
Angle Z is at vertex Z.
- Adjacent side to Z: YZ = 24
- Hypotenuse: XZ = 30
→ cos Z = adjacent/hypotenuse = 24/30 =
4/5
---
10) tan C
Triangle ABC, right-angled at B.
Angle C is at vertex C.
- Opposite side to C: AB = 27
- Adjacent side to C: BC = 36
→ tan C = opposite/adjacent = 27/36 =
3/4
---
Final Answer:
1) 3/4
2) 8/17
3) 4/5
4) 4/3
5) 15/17
6) 4/5
7) 3/5
8) 7/25
9) 4/5
10) 3/4
Parent Tip: Review the logic above to help your child master the concept of trigonometric ratios sohcahtoa worksheet.
