Question

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

Answer 1

Applying Pythagoras theorem for $ΔABC,$we obtain
$\text{AC}^ 2 =\text{ AB}^ 2 + \text{BC}^ 2$
$= (24\text{ cm})^2 + (7 \text{cm})^ 2$
$= (576 + 49)$cm2
$= 625$ cm2
$∴$ AC = $\sqrt{625}$ cm = 25 cm

(i)

$\text{ sin A} = \frac{\text{Side}\ \text{ Opposite}\ \text{ to}\ ∠A }{\text{Hypotenuse}}$ $= \frac{\text{BC}}{\text{AC}} = \frac{7}{25}$

\text{ Cos A} = \frac{\text{Side}\ \text{ Adjacent}\ \text{ to}\ ∠A }{\text{Hypotenuse}}$$= \frac{\text{AB}}{\text{AC}} = \frac{24}{25}

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**(ii) **

$\text{ sin C} = \frac{\text{Side}\ \text{ Opposite}\ \text{ to}\ ∠C }{\text{Hypotenuse}}$e $= \frac{\text{AB}}{\text{AC}} = \frac{24}{25}$

\text{ Cos C} = \frac{\text{Side}\ \text{ Adjacent}\ \text{ to}\ ∠C }{\text{Hypotenuse}}$$= \frac{\text{BC}}{\text{AC}} = \frac{7}{25}