Calculate sides

In the triangle, the side length AB = 6 cm, the height to side c = 5 cm, and the angle BCA = 35°. Calculate sides a b.

Correct answer:

a = 5.455 cm
b = 9.5881 cm

c = 6 cm v_{1} = 5 cm γ = 35^{\circ} S = \frac{c \cdot v _{1}}{2} = \frac{6 \cdot 5}{2} = 15 cm^{2} tan α = v_{1} : c_{1} tan β = v_{1} : c_{2} c_{1} + c_{2} = c α + β + γ = 180 ° c_{1} \cdot tan α = v_{1} c_{2} \cdot tan (145 ° - α) = v_{1} c_{1} + c_{2} = c c_{1} \cdot tan α = v_{1} (c - c_{1}) \cdot tan (145 ° - α) = v_{1} c_{1} \cdot tan α = 5 (6 - c_{1}) \cdot tan (145 ° - α) = 5 α = 0.548585 ≐ 0.5486 rad A = α \to ° = α \cdot \frac{1 8 0}{π} ° = 0.5486 \cdot \frac{1 8 0}{π} ° = 31.43161 ° β = 145 / 180 π - α = 145 / 180 \cdot 3.1416 - 0.5486 ≐ 1.9821 rad B = β \to ° = β \cdot \frac{1 8 0}{π} ° = 1.9821 \cdot \frac{1 8 0}{π} ° = 113.56839 ° c_{1} = v_{1} / tan α = 5 / tan 0.5486 ≐ 8.1812 cm c_{2} = c - c_{1} = 6 - 8.1812 ≐ - 2.1812 cm cos β = c_{2} : a a = c_{2} / cos β = (- 2.1812) / cos 1.9821 = 5.455 cm

cos α = c_{1} : b b = c_{1} / cos α = 8.1812 / cos 0.5486 = 9.5881 cm

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