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Question
In ∆ ABC, if a = 18, b = 24 and c = 30, find cos A, cos B and cos C.
Solution
\[\text{ Given }: a = 18, b = 24 \text{ and } c = 30 . \]
\[\cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{576 + 900 - 324}{2 \times 24 \times 30} = \frac{1152}{1140} = \frac{4}{5}\]
\[\cos B=\frac{a^2 + c^2 - b^2}{2ac}=\frac{324 + 900 - 576}{2 \times 18 \times 30}= \frac{648}{1080} =\frac{3}{5}\]
\[\cos C=\frac{a^2 + b^2 - c^2}{2ab}=\frac{576 + 324 - 900}{2 \times 24 \times 18}=0\]
Hence, \[\cos A = \frac{4}{5}, \cos B=\frac{3}{5}, \cos C= 0\]
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