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

Consider the figure above,

From Pythagoras theorem,

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

$A{C}^2={24}^2+7^2$

$A{B}^2=576+49=625$

$AB=25$

Solution(i):

$\sin \theta =\frac{oppositeSide}{Hypotenuse}$

$\sin A=\frac{BC}{AC}=\frac{7}{25}$

$\cos \theta =\frac{AdjacentSide}{Hypotenuse}$

$\cos A=\frac{AB}{AC}=\frac{24}{25}$

Solution(ii):

$\sin C=\frac{AB}{AC}=\frac{24}{25}$

$\cos C=\frac{BC}{AC}=\frac{7}{25}$