Oblicz w trojkacie ABC dlugosc strony b oraz wielkosc katu przy pomocy twierdzenia sinusow. Dane: a.... Question from @meega

November 2018 1 136 Report

Oblicz w trojkacie ABC dlugosc strony b oraz wielkosc katu $\beta$ przy pomocy twierdzenia sinusow.
Dane: a= 15 cm, c= 28 cm, $\gamma$ =77°
Szukane: b= ?, $\beta = ?$

animaldk $Rysunek\ pogladowy\ w\ zalaczniku.\\\\a=15cm;\ c=28cm;\ \gamma=77^o\\\\Z\ tw\ sinusow\ mamy:\\\\\frac{a}{sin\alpha}=\frac{c}{sin\gamma};\ sin77^o\approx0,9744\\\\\frac{15}{sin\alpha}=\frac{28}{0,9744}\\\\28sin\alpha=14,616\ /:28\\\\sin\alpha=0,522\\\\\alpha\approx31,5^o$

$\beta=180^o-(77^o+31,5^o)=71,5^o\\\\\frac{b}{sin\beta}=\frac{c}{sin\gamma};\ sin71,5^o\approx0,3173\\\\\frac{b}{0,3173}=\frac{28}{0,9744}\ /\cdot0,3173\\\\b\approx9,12\ (cm)$

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