The missing diagram is attached below
Answer:
The length of XY is 10 units
The value of sin (X) is [tex]\frac{4}{5}[/tex]
The value of cos (X) is [tex]\frac{3}{5}[/tex]
The value of tan (X) is [tex]\frac{4}{3}[/tex]
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 = [tex]\frac{opposite}{hypotenuse}[/tex]
cos X = [tex]\frac{adjacent}{hypotenuse}[/tex]
tan X = [tex]\frac{opposite}{adjacent}[/tex]
∵ The side opposite to ∠X is YZ
∵ The side adjacent to ∠ X is XZ
∵ The hypotenuse is XY
∴ sin X = [tex]\frac{YZ}{XY}[/tex]
∴ cos X = [tex]\frac{XZ}{XY}[/tex]
∴ tan X = [tex]\frac{YZ}{XZ}[/tex]
∵ YZ = 8 and XY = 10
∴ sin X = [tex]\frac{8}{10}[/tex]
- Reduce it to its lowest term
∴ sin (X) = [tex]\frac{4}{5}[/tex]
∴ cos X = [tex]\frac{6}{10}[/tex]
- Reduce it to its lowest term
∴ cos (X) = [tex]\frac{3}{5}[/tex]
∴ tan X = [tex]\frac{8}{6}[/tex]
- Reduce it to its lowest term
∴ tan (X) = [tex]\frac{4}{3}[/tex]
