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

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#### Solution

We have

α=90°

β=60°

γ=θ

Since cos^{2}α+cos^{2}β+cos^{2}γ=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°`

Concept: Properties of Inverse Trigonometric Functions

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