JAMB - Mathematics (1993 - No. 31)
If two angles of a triangle are 30° each and the longest side is 10cm. Calculate the length of each of the other sides.
5cm
4cm
3√3 cm
\(\frac{10\sqrt{3}}{3}\)cm
ব্যাখ্যা
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