Triangle - sines

The sum of the lengths of the two sides b + c = 12 cm
Beta angle = 68
Gamma angle = 42
draw triangle ABC

Correct answer:

a = 7.064 cm
b = 6.9699 cm
c = 5.0301 cm

b + c = 12 β = 68^{\circ} γ = 42^{\circ} α = 180 - β - γ = 180 - 68 - 42 = 70^{\circ} b : c = sin β : sin γ k = sin β / sin γ = sin 68 ° / sin 42 ° = 0.927184 / 0.669131 = 1.38565 b + c = 12 b = k \cdot c b + c = 12 b = 1.3856545280631 \cdot c b + c = 12 b - 1.385655 c = 0 R o w 2 - R o w 1 \to R o w 2 b + c = 12 - 2.39 c = - 12 c = \frac{- 1 2}{- 2 . 3 8 5 6 5 4 5 3} = 5.03006611 b = 12 - c = 12 - 5.03006611 = 6.96993389 b = 6.969934 c = 5.030066 a = b^{2} + c^{2} - 2 \cdot b \cdot c \cdot cos α = b^{2} + c^{2} - 2 \cdot b \cdot c \cdot cos 70 ° = 6.969 9^{2} + 5.030 1^{2} - 2 \cdot 6.9699 \cdot 5.0301 \cdot cos 70 ° = 6.969 9^{2} + 5.030 1^{2} - 2 \cdot 6.9699 \cdot 5.0301 \cdot 0.34202 = 7.064 = 7.064 cm

c = 5.0301 ≐ 5.0301 cm Verifying Solution: s = b + c = 6.9699 + 5.0301 = 12

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