Makes no sense as theta is obviously obtuse

[synkk]

Working for a)

Resolving upwards:

12cos(θ -90) - 8 = 0
cos(θ-90) = sinθ
12sinθ = 8
sinθ = 2/3
θ = 41.8 (3.sf)

This makes no sense as theta is obviously obtuse, if I don't simplify to sinθ I get:

cos(θ-90) = 2/3
θ = 48.2... + 90
= 138.2 (1.dp)

Why does it not work if I simplify to sinθ?

 

[Villyer]

sinθ = 2/3 has an infinite number of solutions, what are some others?

 

[synkk]

sinθ = 2/3 has an infinite number of solutions, what are some others?

180 - θ

silly me, thanks.