θ could be one of two complementary angles, so I’ll start with one angle and then complement it in case you meant the other angle.
First, let’s calculate the length of the remaining side:
√(48-(2√10)²)=√(48-40)=√8=2√2.
(a)
sinθ=2√10/√48=2√(10/48)=2√/(5/24)=√⅚; cosecθ=√⁶⁄₅ or √1.2.
cosθ=2√2/√48=2√(1/24)=√⅙; secθ=√6.
tanθ=sinθ/cosθ=√5; cotθ=√5/5 (same as 1/√5).
(b)
θ=arctan(√5)=65.9, or 66° to the nearest degree.
The “other” θ is 24° to the nearest degree and the trig ratios are:
(a)
sinθ=√⅙; cosecθ=√6.
cosθ=√⅚; secθ=√⁶⁄₅ or √1.2.
tanθ=√5/5 (same as 1/√5); cotθ=√5.