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$\Delta X Y Z$ has lengths 4,5 and 6 as shown in the diagram. Use the cosine rule, show that $\cos \widehat{Y}+\cos \widehat{Z}=\frac{7}{8}$.

in Mathematics by Diamond (75,918 points) | 32 views

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$$4^{2}=5^{2}+6^{2}-2(5)(6) \cos Y $$
$$\therefore 16=25+36-60 \cos Y$$

\therefore \cos Y=\frac{45}{60} \\
\therefore \cos Y=\frac{3}{4}  \\
6^{2}=4^{2}+5^{2}-2(4)(5) \cos Z  \\
\therefore \cos Z=\frac{5}{40} \\
\cos Z=\frac{1}{8} \\
\therefore \cos \hat{Y}+\cos \hat{Z}=\frac{3}{4}+\frac{1}{8}=\frac{7}{8}
by Diamond (75,918 points)

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