Question

In a right angled triangle, as shown below, if AB=3 cm, BC=4 cm then what is the value of cos A?

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{3}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A

$\frac{3}{5}$

Since ABC is a right angled triangle, we can apply Pythagoras theorem to get the length of side AC (hypotenuse).
Therefore, $A{C}^2=A{B}^2+B{C}^2$
$\Rightarrow A{C}^2=3^2+4^2$
$\Rightarrow A{C}^2$ = 9 + 16 = 25
$\Rightarrow$ AC = $\sqrt{2}5$ = 5
$\Rightarrow$ AC = 5
Now, cos A = $\frac{AB}{AC}$ = $\frac{3}{5}$.