Question

Cum aflu aria triunghiului ABC daca stiu ca masura lui B=45° masura lui C=60° si BC=8 cm???

Answer 1

Folosim formula $S=\dfrac{a^2 sinB sinC}{2 sinA}$ si observam ca unghiul A are masura de 180-45-60 =75 grade, iar
sin75=sin(30+45)=sin30cos45+sin45cos30=1/2·√2/2+√2/2·√3/2=√2/4(1+√3)

Deci $S=\dfrac{BC^2\ sinB\ sinC}{2\ sinA}=\dfrac{8\cdot\dfrac{\sqrt2}{2}\cdot \dfrac{\sqrt3}{2}}{2\cdot\dfrac{\sqrt2}{4}(\sqrt3+1)}}=\dfrac{4\sqrt3}{\sqrt3+1}=\dfrac{4\sqrt3(\sqrt3-1)}{2}=$

$=2(\sqrt3-3)$