Question

Please help on this question?

Answer 1

Hi there,

θ = 180º + the angle of the right-angled triangle.

For finding the angle we know that the opposite side measures 6 units and the adjacent side measures 8 units. So, the hypotenuse is 10 units.

If we want to find the angle of the right-angled triangle we have to use the following equation.

sin(the angle of the right-angled triangle) =
`(6)/(10)`

⇒ the angle of the right-angled triangle =
`sin^(-1)((6)/(10))` ≈ 36,87º

So,

θ = 180º + the angle of the right-angled triangle

θ ≈ 180º + 36,87º

θ ≈ 216,87º

sin(θ) = sin(216,87º)

sin(θ) =
`(-6)/(10)`

sin(θ) =
`(-3)/(5)`

If you want to do it using properties:

θ = 180º + |the angle of the right-angled triangle|

⇒ sin(θ) = sin(180º + |the angle of the right-angled triangle|)

Using properties:

⇒ sin(θ) = sin(180º)*cos( |the angle of the right-angled triangle|) + cos(180º)*sin(|the angle of the right-angled triangle|)

Sin (180) = 0

⇒ sin(θ) = cos(180º)*sin(|the angle of the right-angled triangle|)

sin(the angle of the right-angled triangle) = -
`(6)/(10)`

And cos(180º) = -1

⇒ sin(θ) = -1*
`(6)/(10)`

⇒ sin(θ) =
`(-6)/(10)`

⇒ sin(θ) =
`(-3)/(5)`