Question

Not ConnectedThunde...lt BridgeNot Connected2 (07.01 HC)answer the following question. Find the value of sin x and cosy. What relationship do the ratios of sin x® and cos yº share?

Answer 1

The given triangle is a right-angled triangle.

Consider PO is Hypotenuse.

By using the Pythagoras formula, we get

`PO^2=8^2+6^2`

`PO^2=64+36`
`PO^2=100=10^2`
`PO=10`

Consider the angle x:

Recall the sine formula

`\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}`

Substitute Opposite side =6 and Hypotenuse=10, we get

`\sin x^o=(6)/(10)`

`\sin x^o=(3)/(5)`
`\text{Use sin }36.869=(3)/(5)`

`\sin x^o=\sin 36.869`
`x^o=37`

Consider the angle y:

Recall the sine formula

`\sin \theta=\frac{Opposite\text{ side}}{\text{Hypotenuse}}`

Substitute Opposite side =8 and Hypotenuse=10, we get

`\sin y^o=(8)/(10)`

`\sin y^o=(4)/(5)`

`\text{Use }\sin 53.13^{}=(4)/(5)`

`\sin y^o=\sin \text{ 53.13}`
`y^o=53^{}`

Hence the required values are

`x^o=37^o`
`y^o=53^o`