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 \(= \frac{\text{AB}}{\text{AC}} = \frac{24}{25}\)

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