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Question
In ∆ABC, if a = 18, b = 24 and c = 30 and ∠c = 90°, find sin A, sin B and sin C.
Solution
Given,∠C = 90°, a = 18, b = 24 and c = 30
According to sine rule, \[\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\]
\[\Rightarrow \frac{c}{\sin C} = \frac{a}{\sin A}\]
\[ \Rightarrow \sin A = \frac{a\sin C}{c}\]
\[ = \frac{18 \times \sin\left( 90° \right)}{30}\]
\[ = \frac{18}{30}\]
\[ = \frac{3}{5}\]
\[Also, \frac{b}{\sin B} = \frac{c}{\sin C}\]
\[ \Rightarrow \sin B = \frac{b\sin C}{c}\]
\[ = \frac{24\sin90°}{30}\]
\[ = \frac{24}{30}\]
\[ = \frac{4}{5}\]
\[and\]
\[ \sin C = \sin90° = 1\]
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