Using the given quantities for the sides a and b as well as for the angle γ the length of the unknown third side c can be calculated with the help of the general cosine theorem for c.
Formula: Cosine theorem for c
c² = a² + b² − 2ab × cos γ°
and converted to c
c = a² + b² − 2ab × cos γ°
Inserting the existing values
Inserting the values a = 4, b = 6 and γ = 70°, we obtain
c = 4² + 6² − 2 × 4 × 6 × cos 70° ≈ 5.97
Solution
The missing third side c has a length of 5.97 in.