Answer:
16.6°
Step-by-step explanation:
The triangle can be solved using the Law of Cosines to find the side opposite the given angle, then the Law of Sines to find the missing angle from the given sides.
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We choose to use a=10, b=4, C=29°.
c² = a² +b² -2ab·cos(C) . . . . . law of cosines
c² = 10² +4² -2·10·4·cos(29°) ≈ 46.0304
c ≈ √46.0304 ≈ 6.78457
Then angle B (opposite side b) is ...
sin(B)/b = sin(C)/c . . . . . . . . . law of sines
sin(B)/4 = sin(29°)/6.78457
B = arcsin(4/6.78457×sin(29°)) ≈ 16.6085°
The missing acute angle is about 16.6°.
