Cosine

Cosine and sine theorem:
Calculate all unknown values (side lengths or angles) from triangle ABC.
c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm

Final Answer:

α =  138 °
a =  8.0211 cm
b =  5.6277 cm

Step-by-step explanation:

$$\begin{gathered} c=2.9\text{cm} \\ \beta =28{}^{\circ } \\ \gamma =14{}^{\circ } \\ \alpha +\beta +\gamma =180° \\ \alpha =180-\beta -\gamma =180-28-14=138^{\circ } \end{gathered}$$

$$\begin{gathered} a:c=\sin \alpha :\sin \gamma \\ a=c\cdot \frac{\sin \alpha }{\sin \gamma }=c\cdot \frac{\sin 138°}{\sin 14°}=2.9\cdot \frac{\sin 138°}{\sin 14°}=2.9\cdot \frac{0.669131}{0.241922}=8.021=8.0211\text{cm} \end{gathered}$$

$$\begin{gathered} b:c=\sin \beta :\sin \gamma \\ b=c\cdot \frac{\sin \beta }{\sin \gamma }=c\cdot \frac{\sin 28°}{\sin 14°}=2.9\cdot \frac{\sin 28°}{\sin 14°}=2.9\cdot \frac{0.469472}{0.241922}=5.628=5.6277\text{cm} \end{gathered}$$

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