I will solve this trigonometry worksheet by calculating the value of each trigonometric ratio for the given right triangles. I'll use the basic definitions: sine (sin) = opposite/hypotenuse, cosine (cos) = adjacent/hypotenuse, and tangent (tan) = opposite/adjacent.
Let me work through each problem one by one:
1) tan Z in triangle XYZ
- Opposite to angle Z is side XY = 21
- Adjacent to angle Z is side YZ = 28
- tan Z = 21/28 = 3/4
2) cos C in triangle ABC
- Adjacent to angle C is side BC = 16
- Hypotenuse is AC = 34
- cos C = 16/34 = 8/17
3) sin C in triangle ABC
- Opposite to angle C is side AB = 28
- Hypotenuse is AC = 35
- sin C = 28/35 = 4/5
4) tan X in triangle XYZ
- Opposite to angle X is side YZ = 32
- Adjacent to angle X is side XY = 24
- tan X = 32/24 = 4/3
5) cos A in triangle ABC
- Adjacent to angle A is side AB = 16
- Hypotenuse is AC = 34
- cos A = 16/34 = 8/17
6) sin A in triangle ABC
- Opposite to angle A is side BC = 24
- Hypotenuse is AC = 40
- sin A = 24/40 = 3/5
7) sin Z in triangle XYZ
- Opposite to angle Z is side XY = 24
- Hypotenuse is XZ = 40
- sin Z = 24/40 = 3/5
8) sin C in triangle ABC
- Opposite to angle C is side AB = 14
- Hypotenuse is AC = 50
- sin C = 14/50 = 7/25
9) cos Z in triangle XYZ
- Adjacent to angle Z is side YZ = 18
- Hypotenuse is XZ = 30
- cos Z = 18/30 = 3/5
10) tan C in triangle ABC
- Opposite to angle C is side AB = 27
- Adjacent to angle C is side BC = 36
- tan C = 27/36 = 3/4
Here are the final answers:
1) tan Z = 3/4
2) cos C = 8/17
3) sin C = 4/5
4) tan X = 4/3
5) cos A = 8/17
6) sin A = 3/5
7) sin Z = 3/5
8) sin C = 7/25
9) cos Z = 3/5
10) tan C = 3/4
Parent Tip: Review the logic above to help your child master the concept of geometry trigonometric ratios worksheet.
