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Calculate the area of triangle ABC, if given by alpha = 49°, beta = 31°, and the height on the c side is 9cm.

Correct answer:

S =  102.6094 cm²

Step-by-step explanation:

$$\begin{gathered} \alpha =49\text{ ° } \\ \beta =31\text{ ° } \\ h=9\text{ cm } \\ \tan \alpha =h:c_1 \\ {c}_1=h\mathrm{/}\tan \alpha \mathrm{°}=h\mathrm{/}\tan 49\mathrm{°}=9\mathrm{/}\tan 49\mathrm{°}=9\mathrm{/}1.150368=7.82358\text{ cm } \\ \tan \beta =h:c_2 \\ {c}_2=h\mathrm{/}\tan \beta \mathrm{°}=h\mathrm{/}\tan 31\mathrm{°}=9\mathrm{/}\tan 31\mathrm{°}=9\mathrm{/}0.600861=14.97852\text{ cm } \\ c=c_1+c_2=7.8236+14.9785\doteq 22.8021\text{ cm } \\ S={\displaystyle \frac{c\cdot h}{2}}={\displaystyle \frac{22.8021\cdot 9}{2}}=102.6094{\text{cm}}^2 \end{gathered}$$

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