Question

In $\Delta ABC$, $\angle C={30}^{\circ },\angle B={80}^{\circ },\angle A={70}^{\circ },AB=12cm$ as shown in the figure. The length of the side AC is equal to ___

$\left[\begin{array}{c}sin{30}^{\circ }=0.5\\ sin{70}^{\circ }=0.93\\ sin{80}^{\circ }=0.98\end{array}\right]$

• A. 26.8 cm
• B. 20.95 cm
• C. 21.8 cm
• D. 23.63 cm

Answer 1

The correct option is D

23.63 cm

Draw diameter AD passing through centre O and connect DB

$\angle D={30}^{\circ }$ (Angle subtended by the same chord AB)

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

In right - angled triangle ABD

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

$AD=\frac{AB}{sin{30}^{\circ }}=\frac{12}{0.5}=d=24cm...\left(1\right)$

In $\Delta ABC,$ applying sine rule

$\frac{AC}{sin{80}^{\circ }}=\frac{AB}{sin{30}^{\circ }}=d=24cm$...( from (1))

$AC=24\times sin{80}^{\circ }=23.63cm$