Question

HELP PLEASE. I'm having a hard time solving this question

Answer 1

cos θ = -
`√(2)` / 6

sin θ =
`\sqrt{1-(2)/(6) }`

sin θ =
`\sqrt{(4)/(6) }`

sin θ = 2/
`√(6)`

tan β = 5/12

sin β = 5/5

cos β = 12/5

sin ( θ + β ) = sin θ cos β + cos θ sin β

sin ( θ + β ) = 2/
`√(6)` * 12/5 + ( -
`√(2)` / 6 ) * 5/5

sin ( θ + β ) = 2/2.44 * 2.4 + 1.414/6 * 1

sin ( θ + β ) = 0.8196 * 2.4 + 0.2356 * 1

sin ( θ + β ) = 1.96 + 0.2356

sin ( θ + β ) = 2.1956