# Two corners of a triangle have angles of #(5 pi ) / 12 # and # ( pi ) / 8 #. If one side of the triangle has a length of #4 #, what is the longest possible perimeter of the triangle?

##### 2 Answers

#### Explanation:

Let in

For maximum perimeter of triangle , we must consider the given side of length

Now, using Sine rule in

hence, the maximum possible perimeter of the

I will let you do the final calculation.

#### Explanation:

Sometimes a quick sketch helps in the understanding of the problem. That is the case hear. You only need to approximate the two given angles.

It is immediately obvious (in this case) that the shortest length is AC.

So if we set this to the given permitted length of 4 then the other two are at their maximum.

The most straight forward relationship to use is the sine rule.

We start be determining the angle A

Known:

This gives:

Thus

and

Work these out and add then all up including the given length of 4