Home > Student Resources > 30 – 60 – 90 Triangles

30 – 60 – 90 Triangles

$If\ \triangle ABC\ is\ an\ isosceles\ triangle,\ what\ is\ the\ length\ of\ BD?$

$\angle CAD=30\degree$

$\overline{AD}=10$

$180\degree =90\degree +30\degree +x\degree$

$x=60\degree$

$\overline{AC}=\frac{1}{2}\times hyp.\times\sqrt{3}=\frac{1}{2}\times 10\times\sqrt{3}=5\sqrt{3}$

$\overline{CD}=\frac{1}{2}\times hyp.=\frac{1}{2}\times 10=5$

$\overline{CB}-\overline{CD}=\overline{BD}$

$5\sqrt{3}-5=\overline{BD}$

$5(1.732)-5=\overline{BD}$

$8.666-5=\overline{BD}$

$3.66=\overline{BD}$