Question

In a $\Delta ABC$, right angled at $B,$ if $AB=12$ and $BC=5$, find:
(i) $sinA$ and $tanB$

Answer 1

By Pythagoras theorem, we have

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

TRIGONOMETRIC RATIOS

$\Rightarrow A{C}^2={12}^2+5^2$

$\Rightarrow A{C}^2=169$

$\Rightarrow AC=13$

(i) When we consider t-ratios of $\angle A$, we have

Base $=AB=12,$ Perpendicular $=BC=5$

and, Hypotenuse$=AC=13$

$\therefore$ $sinA=\frac{Perpendicular}{Hypotenuse}$ $=\frac{5}{13}$

$tanA=\frac{Perpendicular}{Base}=\frac{5}{12}$