Answer:
tan(α+β) ≈ 5.8498
Explanation:
tan(α+β) = tan(arccos(0.637) +arcsin(0.498)) = tan(50.4315° +29.8677°)
= tan(80.2993°) ≈ 5.8498
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Comment on this working
You may be expected to use trig identities to find ...
tan(α) = √(1-cos²(α))/cos(α)
tan(β) = sin(β)/√(1-sin²(β))
tan(α+β) = (tan(α)+tan(β))/(1 -tan(α)tan(β))
Or
sin(α) = √(1-cos²(α))
cos(β) = √(1 -sin²(β))
tan(α+β) = sin(α+β)/cos(α+b)
= (sin(α)cos(β) +cos(α)sin(β))/(cos(α)cos(β) -sin(α)sin(β))
Either way, a calculator is definitely involved. Since a calculator is required for the solution, it is far easier to do the problem using inverse trig functions.