Question

In Triangle $ABC,AB=15cm,AC=8cm,\angle A={50}^{\circ },$ as shown below.The length of BC will be equal to $[sin{50}^{\circ }=0.76,cos{50}^{\circ }=0.64]$

• A. 13.9 cm
• B. 12.5 cm
• C. 11.6 cm
• D. 10.2 cm

Answer 1

The correct option is C

11.6 cm

Drawn CD perpendicular to AB

in Right-angled triangle ADC

$sin{50}^{\circ }=\frac{CD}{AC}$

$CD=ACsin{50}^{\circ }=8\times 0.76=6.08$

$cos{50}^{\circ }=\frac{AD}{AC}$

$AD=ACcos{50}^{\circ }=8\times 0.64=5.12$

$DB=AB-AD$

$DB=15-5.12=9.88cm$

In right-angled triangle CBD

$B{C}^2=D{B}^2+C{D}^2$

$B{C}^2=(9.88{)}^2+(6.08{)}^2$

$\sqrt{97.61+36.966}$

$BC=\sqrt{134.57}=11.6cm$