Answer is a = 5.8'' and b = 1.5''
Sine and cos Formula:
The sin formula is given as: sin θ = Perpendicular side / Hypotenuse side.
The cos formula is given as: cos θ = Adjacent side / Hypotenuse side.
Here,
ABC is a right-angled triangle with angle c = 90 degrees.
Given, ∠B = 14.5° and c = 6''
Now, cosB = BC / AB
=> cos(14.5°) = a / c
=> a = 6 * cos(14.5°) = 6 * 0.97
=> a = 5.8''
Again, sinB = AC / AB
=> sin(14.5°) = b / c
=> b = 6 * sin(14.5°)
=> b = 1.5''
Hence, a = 5.8'' and b = 1.5''
Learn more about sine, cos and tan Formulas here:
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