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) = [tex]\frac{6}{10}[/tex]
⇒ the angle of the right-angled triangle = [tex]sin^{-1}(\frac{6}{10})[/tex] ≈ 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) = [tex]\frac{-6}{10}[/tex]
sin(θ) = [tex]\frac{-3}{5}[/tex]
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) = -[tex]\frac{6}{10}[/tex]
And cos(180º) = -1
⇒ sin(θ) = -1* [tex]\frac{6}{10}[/tex]
⇒ sin(θ) = [tex]\frac{-6}{10}[/tex]
⇒ sin(θ) = [tex]\frac{-3}{5}[/tex]
