Question

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

Answer 1

We have

α=90° 

β=60°

γ=θ

Since cos²α+cos²β+cos²γ=1,

`cos^2(90°)+cos^2(60°)+cos^2θ=1  `

`0^2+(1/2)^2+cos^2θ=1`

`cos^2θ=1−1/4=3/4`

`cosθ=sqrt3/2                    (θ is acute.)`

`∴ θ=30°`