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 ΔABC, right angled at B. AB = 24 cm, BC = 7 cm. Determine:
(i) sin A cos A,
(ii) sin C, cos C.

Let AB = 24 cm

BC = 7cm 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 = 25 cm

Now,
$\left(i\right)sinA=\frac{BC}{AC}=\frac{7}{25}\left(ii\right)cosA=\frac{AB}{AC}=\frac{24}{25}\left(iii\right)sinC=\frac{AB}{AC}=\frac{24}{25}\left(iv\right)cosC=\frac{BC}{AC}=\frac{7}{25}$