In ∆ABC, if a = 18, b = 24 and c = 30 and ∠c = 90°, find sin A, sin B and sin C.

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Solution

Given,∠C = 90°, a = 18, b = 24 and c = 30

According to sine rule, $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ .

$\Rightarrow \frac{c}{\sin C} = \frac{a}{\sin A} \Rightarrow \sin A = \frac{a \sin C}{c} = \frac{18 \times \sin (90 °)}{30} = \frac{18}{30} = \frac{3}{5} Also, \frac{b}{\sin B} = \frac{c}{\sin C} \Rightarrow \sin B = \frac{b \sin C}{c} = \frac{24 \sin 90 °}{30} = \frac{24}{30} = \frac{4}{5} and \sin C = \sin 90 ° = 1$

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