Question

In the adjoining figure, ΔABC is a right-angled triangle in which ∠B = 90⁰, ∠30⁰ and AC = 20cm. Find (i) BC, (ii) AB. 

Answer 1

From the given right-angled triangle, we have:

${\displaystyle \frac{BC}{AC}={\sin 30}^0}$

⇒${\displaystyle \frac{BC}{20}=\frac{1}{2}}$ 

⇒BC = ${\displaystyle \frac{20}{2}=10cm}$

Also, ${\displaystyle \frac{AB}{AC}={\cos 30}^0}$

⇒${\displaystyle \frac{AB}{20}=\frac{\sqrt{3}}{2}}$

⇒${\displaystyle AB=(20\times \frac{\sqrt{3}}{2})=10\sqrt{3}cm}$

∴ BC = 10cm and AB = 10${\displaystyle \sqrt{3}}$ cm