Question

We can cut out a triangle of side 8 cm whose opposite angle is ${30}^{\circ }$ from a circular sheet of diameter $16cm[sin{30}^{\circ }=0.5]$

• A. True
• B. False

Answer 1

The correct option is A

True

Let ABC be the triangle and $BC=8cm,\angle A={30}^{\circ }$

Draw diameter BD passing through centre 0. and join DC

$\angle BAC=\angle BDC$ ( Angle subtended by the same chord BC)

$\angle BCD={90}^{\circ }$ (Angle subtended by the diameter on the circumference)

In right angled triangle BDC

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

$BD=\frac{BC}{sin{30}^{\circ }}=\frac{8}{0.5}=16$

Hence, the diameter BD = 16 cm

Therefore, the given statement is correct.