Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
Answer each of the following questions in one word or one sentence or as per exact requirement of the question.
In ∆ABC, if a = 8, b = 10, c = 12 and C = λA, find the value of λ.
Using cosine rule, we have
$\cos A=\frac{b^{2}+c^{2}-a^{2}}{2 b c}$
$\Rightarrow \cos A=\frac{10^{2}+12^{2}-8^{2}}{2 \times 10 \times 12}$
$\Rightarrow \cos A=\frac{100+144-64}{240}$
$\Rightarrow \cos A=\frac{180}{240}=\frac{3}{4} \quad \ldots .(1)$
Now, using sine rule, we have
$\frac{a}{\sin A}=\frac{c}{\sin C}$
$\Rightarrow \frac{8}{\sin A}=\frac{12}{\sin \lambda A}$
$\Rightarrow \sin \lambda A=\frac{3}{2} \sin A$
$\Rightarrow \sin \lambda A=2 \times \frac{3}{4} \sin A$
$\Rightarrow \sin \lambda A=2 \sin A \cos A$ [Using (1)]
$\Rightarrow \sin \lambda A=\sin 2 A$
$\Rightarrow \lambda=2$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.