If two angles of a triangle are 30° each and the longest side is 10cm. Calculate the length of each of the other sides.

A.

5cm

B.

4cm

C.

3√3 cm

D.

\(\frac{10\sqrt{3}}{3}\)cm

Correct answer is D

Let each of the unknown side be x.

\(10^{2} = x^{2} + x^{2} - 2(x)(x) \cos 120\)

\(100 = 2x^{2} - 2x^{2} \cos 120\)

\(100 = 2x^{2} + x^{2} = 3x^{2}\)

x = \(\sqrt{\frac{100}{3}}\)

= \(\frac{10}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)

x = \(\frac{10\sqrt{3}}{3}\)cm