If a line makes angles 90°, 60°, and θ with x, y, and z-axis respectively, where θ is acute, then find θ.

If α, β, and γ are the angles made by the line with the x, y, and z axes respectively, then
cos²α + cos²β + cos²γ = 1.
Therefore, cos²90° + cos²60° + cos²θ = 1
⇒ cos²θ = 1 - cos²90° - cos²60°
⇒ cos²θ = 1 - 0 - (1/2)²
⇒ cos²θ = 1 - 1/4 = 3/4
⇒ cosθ = √3/2
⇒ θ = 30°