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