Answer
$β = 90°$
Work Step by Step
Use the property of Direction Cosines given here:
$\cos^2 α + \cos^2 β + \cos^2 γ = 1$
Given that $α = 75°$, $γ = 15°$
$\cos^2 (75°) + \cos^2 β + \cos^2 (15°) = 1$
$(0.2588)^2 + \cos^2 β + (0.9659)^2 = 1$
$0.06699+ \cos^2 β + 0.9330 = 1$
$\cos^2 β = 0$
$\cos β= 0$
$β = 90°$
