Question

We can cut out a triangle whose one side is 7cm and the angle opposite to this side is ${40}^{\circ }$ from a circular sheet of diameter 10cm.

$[sin{40}^{\circ }=0.64]$

• A. True
• B. False

Answer 1

The correct option is B

False

Let ABC be the triangle which is circumscribed by a circle where $BC=7cm,and\angle A={40}^{\circ }$

Draw diameter BD passing through the center O, and join DC

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

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

In right angled triangle BDC

$sin{40}^{\circ }=\frac{BC}{BD}$

$BD=\frac{BC}{sin{40}^{\circ }}=\frac{7}{0.64}=10.93cm$

Diameter BD = 10.93 cm.

Hence the given statement is false.