Find the length of the c side of the mathrm Del... - SS2 Mathematics Trigonometric Ratios II Question
Find the length of the c side of the \(\mathrm{\Delta}ABC\) which have \(a = 2.25cm,\ b = 6.24cm\ \)and\(\ \angle C = 78{^\circ}\) using the cosine rule
Using the cosine rule, \(c^{2} = a^{2} + b^{2} - 2ab\cos C\)
\[c^{2} = {2.25}^{2} + {6.24}^{2} - 2(2.25)(6.24)\cos 78\]
\[c^{2} = 5.0625 + 38.9376 - 2(2.25)(6.24)(0.2079)\]
\[c^{2} = 5.0625 + 38.9376 - 5.837832\]
\[c^{2} = 38.162268\]
\[c = \sqrt{38.162268} = 6.18cm\]
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