Question 136

The angles of a triangle are $$30^\circ, 60^\circ$$ and $$90^\circ$$. Then the sides of the triangle are in the ratio

Solution

Let $$\angle$$A = $$30^\circ$$, $$\angle$$B = $$60^\circ$$ and $$\angle$$C = $$90^\circ$$

sin$$30^\circ$$ = $$\frac{BC}{AB}$$

$$\frac{1}{2}$$ = $$\frac{BC}{AB}$$

Let BC = x and AB = 2x

AC = $$\sqrt{AB^{2} - BC^{2}}$$

AC = $$\sqrt{3}x$$

Now,

Required ratio = BC: AC: AB = x: $$\sqrt{3}x$$: 2x = 1: $$\sqrt{3}$$: 2

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