Inner angles

The inner angles of the triangle are 30°, 45°, and 105° and its longest side is 10 cm. Calculate the shortest side length, and write the result in cm up to two decimal places.

Final Answer:

a =  5.18 cm

Step-by-step explanation:

$$\begin{gathered} A=30 \\ B=45 \\ C=105 \\ c=10\text{cm} \\ a/c=\sin (A)/\sin (C)=\sin 30/\sin 105\doteq 1.018 \\ a=c\cdot \sin A/\sin C=c\cdot \sin 30°/\sin 105°=10\cdot \sin 30°/\sin 105°=10\cdot 0.5/0.965926=5.18=5.18\text{cm} \end{gathered}$$

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