Question

In $\Delta ABC$, right-angled at B. AB = 5 cm and $\angle ACB={30}^{\circ }.$ Determine the lengths of the sides BC and AC.

Answer 1

$\tan {30}^{\circ }=\frac{AB}{BC}\Rightarrow BC=\frac{AB}{\tan {30}^{\circ }}$

$BC=5\sqrt{3}$

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

$A{C}^2=5^2+(5\sqrt{3}{)}^2$

$A{C}^2=25+75$

$AC=10$

Hence sides are $5,5\sqrt{3},10cm$