Question

Answer each of the following questions in one word or one sentence or as per exact requirement of for question:

$In\Delta ABC,ifa=8,b=10,c=12andC=\lambda A,\text{find the value of}\lambda .$

Answer 1

$\text{By cosine rule, we know that,}cosA=\frac{b^2+c^2-a^2}{2bc};cosB=\frac{a^2+c^2-b^2}{2ac};cosC=\frac{a^2+b^2-c^2}{2ab}Thus,cosA=\frac{100+144-64}{2\times 10\times 12}=\frac{3}{4}andcosC=\frac{64+100-144}{2\times 8\times 10}=\frac{1}{8}cosA=\frac{3}{4}\Rightarrow A=co{s}^{-1}\left(\frac{3}{4}\right)\Rightarrow A={41.4096}^{\circ }...\left(1\right)cosC=co{s}^{-1}\left(\frac{1}{8}\right)C={82.8192}^{\circ }...\left(2\right)\text{From equation 1 and 2 we have}\text{From equations (1) and (2), we have}C=2A=\lambda =2.$