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JAMB 1993 · UME · Q41

If two angles of a triangle are 30∘30^\circ each and the longest side is 10 cm, calculate the length of each of the other sides.

Worked solution (try it first)
  1. The third angle is 180∘−30∘−30∘=120∘180^\circ - 30^\circ - 30^\circ = 120^\circ.
  2. The longest side, 10 cm, faces it.
  3. Each of the other sides faces a 30∘30^\circ angle.
  4. Sine rule: asin⁡30∘=10sin⁡120∘\dfrac{a}{\sin30^\circ} = \dfrac{10}{\sin120^\circ}.
  5. So a=10×1232a = \dfrac{10 \times \frac12}{\frac{\sqrt3}{2}}
    =103= \dfrac{10}{\sqrt3}.
  6. Rationalise: 1033\dfrac{10\sqrt3}{3} cm, option D.

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