Answer:[tex]cosA = \frac{a+2}{2a}[/tex]
Step-by-step explanation:
Given that the lengths of the sides of a triangle are consecutive integers
Since side cannot be negative we can assume that the sides are
a, a+1 and a+2 where a>0
The largest angle is opposite side a+2 and smallest is angle opposite a
Using sine formula and the given information that the largest angle is twice the smallest angle
we get
[tex]\frac{a}{sin A} =\frac{a+2}{sin 2A}[/tex]
Cross multiply to get
[tex]\frac{sin 2A}{sin A } =\frac{a+2}{a}[/tex]
Since sin 2A = 2sin A cos A
we get
[tex]2cosA = \frac{a+2}{a} \\cosA = \frac{a+2}{2a}[/tex]
