Question

Given: ΔАВС, m∠ACB = 90°,m∠ACD = 30°,AD = 8 cm. Find: CD, Perimeter ΔABC Please solve!

Answer 1

If m ACD = 30 => m DCB = 60.
In triangle ACD:
$sin 30^{o}=sin \frac{AD}{AC} =\ \textgreater \ \frac{1}{2} = \frac{8}{AC} =\ \textgreater \ AC=16$
$CD= 8 \sqrt{3}$
$BC= 16\sqrt{3}$
AC^{2}+CB^{2}=AB^{2} => AB=$\sqrt{1024}$=32.
=> P=16+32+$16 \sqrt{3}$=48 +$16 \sqrt{3}$.