Question

In a $\Delta$ABC, right angled at B, AB=24 cm, BC=7 cm. Determine

(i) sin A, cos A

(ii) sin C, cos C

Answer 1

In $\Delta$ABC, Using Pythagoras theorem, we have
$A{C}^2=A{B}^2+B{C}^2=(24cm{)}^2+(7cm{)}^2=576c{m}^2+49c{m}^2=625c{m}^2$

So, $AC=25cm$

Now,
$\left(i\right)\sin A=\frac{BC}{AC}=\frac{7}{25}\left(ii\right)\cos A=\frac{AB}{AC}=\frac{24}{25}\left(iii\right)\sin C=\frac{AB}{AC}=\frac{24}{25}\left(iv\right)\cos C=\frac{BC}{AC}=\frac{7}{25}$