Question

In a $△$ ABC, right angled at B, AB = 24 cm , BC = 7 cm. The value of SinA is ?

• A. $\frac{24}{7}$
• B. $\frac{25}{7}$
• C. $\frac{7}{24}$
• D. $\frac{7}{25}$

Answer 1

The correct option is D $\frac{7}{25}$

(D) Given: In $△$ ABC, AB = 24 cm, BC = 7cm and $\angle$ ABC = 90${}^{\circ }$

By using Pythagoras theorem in $△$ ABC we have

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

$A{C}^2={24}^2+7^2$

$A{C}^2=576+49$

$A{C}^2=625$

$AC=625$

AC = 25

Hence, Hypotenuse = 25 cm

By definition,

Sin A $=\frac{\text{perpendicular}}{\text{hypotenuse}}$

Sin A $=\frac{BC}{AC}$

Sin A $=\frac{7}{25}$