Law of sines: startfraction sine (uppercase a) over a endfraction = startfraction sine (uppercase b) over b endfraction = startfraction sine (uppercase c) over c endfraction in δabc, c = 5.4, a = 3.3, and measure of angle a = 20 degrees. what are the possible approximate lengths of b? use the law of sines to find the answer. 2.0 units and 4.6 units 2.1 units and 8.7 units 2.3 units and 7.8 units 2.6 units and 6.6 units

First of all, this problem is properly done with the Law of Cosines, which tells us

giving us a quadratic equation for b we can solve.  But let's do it with the Law of Sines as asked.

We have c,a,A so the Law of Sines gives us sin C

There are two possible triangle angles with this sine, supplementary angles, one acute, one obtuse:

Both of these make a valid triangle with A=20°.   They give respective B's:

So we get two possibilities for b:

2.3 units and 7.8 units

Let's check it with the Law of Cosines:

There's a shortcut for the quadratic formula when the middle term is 'even.'

Looks good.

step-by-step explanation:

the first 5 right here the next 5 i will upload as separate question