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 the Pythagorean theorem to \(ΔABC\), we get \(AC^2 = AB^2 + BC^2\). Substituting the given values, \(AC^2 = (24 \text{ cm})^2 + (7 \text{ cm})^2 = 576 \text{ cm}^2 + 49 \text{ cm}^2 = 625 \text{ cm}^2\). Therefore, \(AC = \sqrt{625} \text{ cm} = 25 \text{ cm}\).

(i)

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

\(\cos A = \frac{\text{Side Adjacent to } ∠A}{\text{Hypotenuse}} = \frac{AB}{AC} = \frac{24}{25}\)

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(ii)

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

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