Question

In a ∆ABC, it is given that ∠B = 90°, AB = 24 cm and BC = 7 cm.
Figure

Find the value of
(i) sin A
(ii) cos A
(iii) sin C
(iv) cos C

Answer 1

Using Pythagoras theorem, we get:
AC² = AB² + BC²
⇒ AC²= (24)² + (7)²
⇒ AC² = 576 + 49 = 625
⇒ AC = 25 cm
Now, for T-Ratios of ∠A, base = AB and perpendicular = BC
(i) sin A = $\frac{BC}{AC}=\frac{7}{25}$

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

Similarly, for T-Ratios of ∠C, base = BC and perpendicular = AB
(iii) sin C = $\frac{AB}{AC}=\frac{24}{25}$

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