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

R.E.F image

In $\Delta$ ABC, B is at right angle.

Given, AB=24cm

BC=7cm

using Pythagoras theorem

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

$\Rightarrow (24{)}^2+(7{)}^2=A{C}^2$

$\Rightarrow AC=\sqrt{\left({24}^2\right)+(7{)}^2}=\sqrt{576+49}=\sqrt{625}$

$\Rightarrow AC=25CM$

(i)sin A=$\frac{BC}{AC}$

$=\frac{7}{25}$

cos A=$\frac{AB}{AC}$

$=\frac{24}{25}$

(ii)sin C=$\frac{AB}{AC}$

$=\frac{24}{25}$

cos c=$\frac{BC}{AC}$

=$\frac{7}{25}$