Question

If the sides of a triangle are $4$cm, $5$cm , $6$cm, then ratio of the cosine of the least and the greatest angles is

• A. $6:1$
• B. $2:1$
• C. $3:4$
• D. $5:6$

Answer 1

The correct option is A $6:1$

Let $a,b,c$ be $4\text{cm},5\text{cm},6\text{cm}$ respectively
Angle opposite to longest side is greatest and vice versa.
Hence $\angle A$ is the least and $\angle C$ is the greatest.
So, the cosine of least and greatest angles are:
$\cos A=\frac{b^2+c^2-a^2}{2bc}=\frac{3}{4}$
$\cos C=\frac{a^2+b^2-c^2}{2ab}=\frac{1}{8}$ $\therefore \cos A:\cos C=\frac{3}{4}:\frac{1}{8}=6:1$