In the figure, the side $a$ is resolved into projections of the other two sides on the base. Which projection formula is correct? 
A$a=b\sin C+c\sin B$
B$a=b\cos B+c\cos C$
C$a=b\cos C+c\cos B$
D$a=b+c$
Answer & Solution
Correct answer: C. $a=b\cos C+c\cos B$
By dropping the perpendicular from the शीर्ष vertex to the base, the base $a$ is split into two parts. One part is the projection of side $c$ on the base, equal to $c\cos B$, and the other is the projection of side $b$, equal to $b\cos C$. Adding them gives $a=b\cos C+c\cos B$.
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