Question

Two sides of a triangle are 8cm and 12cm, and the angle between them is ${110}^{\circ }$ as shown in the figure.

Area of the triangle is ___ ($sin{70}^{\circ }=0.93$)

• A. $45.5c{m}^2$
• B. $37.58c{m}^2$
• C. $54.81c{m}^2$
• D. $48.5c{m}^2$

Answer 1

The correct option is B

$37.58c{m}^2$

Extend AB and draw CD perpendicular to AB.

In $\Delta BDC$

$\angle CBD=({180}^{\circ }-{110}^{\circ })={70}^{\circ }$

$sin{70}^{\circ }=\frac{CD}{BC}$

$CD=BC\times sin{70}^{\circ }$

$CD=8\times 0.93=7.51cm$

Area of triangle =$\frac{1}{2}\times AB\times CD$

$=\frac{1}{2}\times 10\times 7.51cm$

$37.58c{m}^2$