In various constructions, you need to use the longer of two segments to construct the radius of a circle. Why do you think this is? What happens if you use the shorter segment?

You posted this earlier, and it still makes no sense, as Steve pointed out in that post.

Are you talking about "construction" as with ruler and compass in geometry.

Are you perhaps trying to construct a triangle ABC, where AB = 10, AC = 4 and angle B = 30°

Yes, ruler and straight-edge, and please this is an over due assignment and it's the only one i have a problem with, helpp!! Thank you

compass and straight-edge** I'm really sorry for boring you or putting you in confusion but I'm making up work for all my 6 classes pleasssee help me with the above question, for it is the last question in the assisgment for geometry please help fast I want 2 turn it in quickly and finish the others. THANK YOU!

BOTHERING** OMG!

Please HELP it's urgent!

In the example I gave you, the altitude will not reach the base.

Notice I took the smaller side as my radius and the arc cannot reach the base.
height/10 = sin30
height = 10sin 30 = 5
so my second side would have to be at least 5

by taking the longer of the 2 given sides, you would be guaranteed to reach the base.
Using my example, and my calculation, you can find the minimum value needed.
My example is called the "ambiguous case"

So, if I use the shorter segment I would be guaranteed to reach the base,

is that the answer?

..Or the longer side..

Wait I don't get it :/

By taking the longer of the 2 given sides, you would be guaranteed to reach the base. If I took the smaller side as my radius and the arc cannot reach the base.

Is that the answer?

Yes