Question

In the right angled triangle shown below, if AB = 3 cm, BC = 4 cm then what is the value of cos A?
[2 Marks]

Answer 1

Since ABC is a right angled triangle, we can apply Pythagoras theorem to get the length of side AC (hypotenuse).
We know, $A{C}^2=A{B}^2+B{C}^2$
[1 Mark]

$\Rightarrow A{C}^2=3^2+4^2$
$\Rightarrow A{C}^2$ = 9 + 16 = 25
$\Rightarrow AC=\sqrt{2}5=5$
$\Rightarrow AC=5$
Now, cos A = $\frac{AB}{AC}$ = $\frac{3}{5}$.
[1 Mark]