The lengths of the sides of a triangle are consecutive integers, and the largest angle is twice the smallest angle. What is the cosine of the smallest angle

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

Cross multiply to get

Since sin 2A = 2sin A cos A

we get

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2