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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