Tentukan besar sudut dan panjang sisi BC segitiga berikut, kemudian hitunglah luasnya

Tentukan besar sudut dan panjang sisi BC segitiga berikut, kemudian hitunglah luasnya !

(Determine the unknown angle and BC side length of the triangle shown, then determine its area!)

Pembahasan

$\angle C=180-30-45$
${\color{white}\angle C}=105^o$

$\frac{BC}{sin30}=\frac{AC}{sin45}$
$\frac{BC}{\frac{1}{2}}=\frac{10}{\frac{1}{2}\sqrt{2}}$
$BC=\frac{10}{\sqrt{2}}=5\sqrt{2}$

Luas segitiga (surface of the triangle)

$L=\frac{1}{2}\times AC\times BC\times sin\angle C$
$L=\frac{1}{2}\times 10\times 5\sqrt{2}\times sin105$
$L=\frac{1}{2}\times 10\times 5\sqrt{2}\times\frac{1}{4}(\sqrt{6}+\sqrt{2})$
$L=\frac{25}{4}\sqrt{2}(\sqrt{6}+\sqrt{2})$
$L=\frac{25}{4}(\sqrt{12}+\sqrt{4})$
$L=\frac{25}{4}(2\sqrt{3}+2)$
$L=\frac{25}{2}(\sqrt{3}+1)\;\textrm{cm}^2$

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