Use the diagram of triangle XYZ to answer the questions. what is the length of side XY? what is the value of sin (X)? what is the value of cos (X)? what is the value of tan (X)?

For the attached diagram

Value of sin (X) =

Value of cos(X) =  

Value of tan(X) =  

Length of Side XY =  3 m

Length of Side YZ =  4 m

Let us consider a right triangle Δ XYZ in order to understand the Terms            ( Diagram attached ) that are asked

let The length of Side XY is given as 3 m

and the Length of Side YZ is 4 m

Value of sin (X) =

Value of cos(X) =

Value of tan(X) =

For more information please refer to the link  below

link

The missing diagram is attached below

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) =

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