# How do you find the missing length of an isosceles triangle given Base = 8 Angle = 30?

Jun 16, 2015

The length of the non-base sides is $\frac{8}{\sqrt{3}}$

#### Explanation:

(see diagram)

If the isosceles triangle is divided into two right-angled triangles, each resulting right-angled triangle has sides with well known proportions, $2 : 1 : \sqrt{3}$
where the $\sqrt{3}$ proportion corresponds to the base (actually half of the base of the original isosceles triangle) and
the $2$ proportion corresponds to the missing length.

$\frac{\text{missing length")/2 = ("half isosceles base}}{\sqrt{3}}$

Since "half isosceles base" $= \frac{8}{2} = 4$

missing length $= \frac{2 \times 4}{\sqrt{3}} = \frac{8}{\sqrt{3}}$