Trigonometry, SMB-067

Find the value of \(\theta\), correct to the nearest minute. (3 marks)

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\(\theta=112^{\circ} 12^{′}\)

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\(\cos A\)	\(= \dfrac{b^2+c^2-a^2}{2bc} \)
\(\cos \theta\)	\(= \dfrac{7.8^2+10.2^2-15.0^2}{2 \times 7.8 \times 10.2}\)
	\(= -0.3778…\)
\(\therefore \theta\)	\(= \cos^{-1} (-0.3778…) \)
	\(=112.199…^{\circ} \)
	\(=112^{\circ} 12^{′}\ \ \text{(nearest minute)} \)