Q1. In $$∆ \ ABC$$ , right angled at B, AB = 24 cm, BC = 7 cm. Determine :

(i) sin A, cos A
(ii) sin C, cos C

Given, in $$∆ \ ABC$$,
AB = 24 cm, BC = 7 cm and right angled at B

By using the Pythagoras theorem, we have

$$AC^2 \ = \ AB^2 \ + \ BC^2$$
=> $$AC^2 \ = \ (24)^2 \ + \ (7)^2$$
=> $$AC^2 \ = \ 576 \ + \ 49 \ = \ 625$$

=>   $$AC \ = \ \sqrt{625} \ = \ 25$$ cm

(i) $$sinA \ = \ \frac{BC}{AC} \ = \ \frac{7}{25}$$      [∵ $$sin\theta \ = \ \frac{P}{H}$$ ]

$$cosA \ = \ \frac{AB}{AC} \ = \ \frac{24}{25}$$      [∵ $$cos\theta \ = \ \frac{B}{H}$$ ]

(ii) $$sinC \ = \ \frac{AB}{AC} \ = \ \frac{24}{25}$$

$$cosC \ = \ \frac{BC}{AC} \ = \ \frac{7}{25}$$