The missing diagram is attached below
Answer:
The length of XY is 10 units
The value of sin (X) is 
The value of cos (X) is 
The value of tan (X) is 
Step-by-step explanation:
In Δ XYZ
∵ ∠Z is a right angle
∴ XY is the hypotenuse
∴ XZ and YZ are the legs of the triangle
- Use Pythagoras Theorem to find the length of XY
∵ (XY)² = (XZ)² + (YZ)²
∵ XZ = 6 units
∵ YZ = 8 units
- Substitute them in the formula above
∴ (XY)² = (6)² + (8)²
∴ (XY)² = 36 + 64
∴ (XY)² = 100
- Take √ for both sides
∴ XY = 10 units
In The right Δ there are trigonometry ratios
sin X = 
cos X = 
tan X = 
∵ The side opposite to ∠X is YZ
∵ The side adjacent to ∠ X is XZ
∵ The hypotenuse is XY
∴ sin X = 
∴ cos X = 
∴ tan X = 
∵ YZ = 8 and XY = 10
∴ sin X = 
- Reduce it to its lowest term
∴ sin (X) = 
∴ cos X = 
- Reduce it to its lowest term
∴ cos (X) = 
∴ tan X = 
- Reduce it to its lowest term
∴ tan (X) = 