Solve the mathrm Delta ABC which have angle A 1... - SS2 Mathematics Trigonometric Ratios II Question
Solve the \(\mathrm{\Delta}ABC\) which have \(\angle A = 145{^\circ},\ \angle B = 23{^\circ}\ \)and\(\ b = 5.02cm\) using the sine rule
First, calculate the \(\angle C\)
\[\angle C = 180{^\circ} - (\angle A + \angle B)\]
\[\angle C = 180{^\circ} - (145{^\circ} + 23{^\circ})\]
\[\angle C = 180{^\circ} - 168{^\circ}\]
\[\angle C = 12{^\circ}\]
From the Sine Rule, \(\frac{a}{\sin A} = \frac{b}{\sin B}\)
\[\frac{a}{\sin 145} = \frac{5.02}{\sin 23}\]
\[\frac{a}{0.5736} = \frac{5.02}{0.3907}\]
\[a = \frac{5.02 \times 0.5736}{0.3907} \approx 7.37cm\]
From the Sine Rule, \(\frac{b}{\sin B} = \frac{c}{\sin C}\)
\[\frac{5.02}{\sin 23} = \frac{c}{\sin 12}\]
\[\frac{5.02}{0.3907} = \frac{c}{0.2079}\]
\[c = \frac{5.02 \times 0.2079}{0.3907} \approx 2.67cm\]
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