Let’s solve each problem step by step.
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Problem 1: sin C = ?
Triangle ABC, right-angled at B.
Sides: AB = 14 (opposite to angle C), BC = 48 (adjacent to angle C), AC = 50 (hypotenuse).
sin C = opposite / hypotenuse = AB / AC = 14 / 50
Simplify: 14 ÷ 2 = 7, 50 ÷ 2 = 25 →
7/25
As decimal: 14 ÷ 50 =
0.28
✔ Final value:
0.28
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Problem 2: sin Z = ?
Triangle XYZ, right-angled at X.
Sides: XY = 24 (opposite to angle Z), XZ = 32 (adjacent to angle Z), YZ = 40 (hypotenuse).
sin Z = opposite / hypotenuse = XY / YZ = 24 / 40
Simplify: divide numerator and denominator by 8 → 3/5
As decimal: 24 ÷ 40 =
0.6
✔ Final value:
0.6
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Problem 3: tan A = ?
Triangle ABC, right-angled at B.
Sides: AB = 20 (adjacent to angle A), BC = 21 (opposite to angle A), AC = 29 (hypotenuse).
tan A = opposite / adjacent = BC / AB = 21 / 20
As decimal: 21 ÷ 20 =
1.05
✔ Final value:
1.05
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Problem 4: tan B = ?
Triangle ABC, right-angled at A.
Sides: AB = 40 (adjacent to angle B), AC = 30 (opposite to angle B), BC = 50 (hypotenuse).
tan B = opposite / adjacent = AC / AB = 30 / 40
Simplify: 3/4 → as decimal: 30 ÷ 40 =
0.75
✔ Final value:
0.75
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Problem 5: cos X = ?
Triangle XYZ, right-angled at Y.
Sides: XY = 21 (adjacent to angle X), YZ = 20 (opposite to angle X), XZ = 29 (hypotenuse).
cos X = adjacent / hypotenuse = XY / XZ = 21 / 29
Calculate: 21 ÷ 29 ≈
0.7241 (rounded to nearest ten-thousandth)
✔ Final value:
0.7241
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Problem 6: cos C = ?
Triangle ABC, right-angled at B.
Sides: AB = 9 (opposite to angle C), BC = 12 (adjacent to angle C), AC = 15 (hypotenuse).
cos C = adjacent / hypotenuse = BC / AC = 12 / 15
Simplify: 4/5 → as decimal: 12 ÷ 15 =
0.8
✔ Final value:
0.8
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Problem 7: sin 77° = ?
Use calculator: sin(77) ≈
0.9744 (to nearest ten-thousandth)
✔ Final value:
0.9744
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Problem 8: tan 17° = ?
Use calculator: tan(17) ≈
0.3057 (to nearest ten-thousandth)
✔ Final value:
0.3057
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Final Answer:
1. sin C = 0.28
2. sin Z = 0.6
3. tan A = 1.05
4. tan B = 0.75
5. cos X = 0.7241
6. cos C = 0.8
7. sin 77° = 0.9744
8. tan 17° = 0.3057
Parent Tip: Review the logic above to help your child master the concept of trig ratios practice worksheet.
