The answer is option c. But angle C is 45 deg. So as smallest angle will correspond to smallest side in the triangle, so i guessed the answer would be less than 4V3 (V is square root, pardon my notation ) which is the side corresponding to 60 deg,which is less than 2V2+2V6 thus i choose option B . So how is it option C

From the looks of it atleast in my opinion we need to use laws to sin to solve this questions (that’s why hate 3rd party test prep). So what you need is the property of sins —> a/sin a = b/sin b =c/sin c

where a,b&c are the sides of triangles and sin (a,b,c) are the angles opposite to those sides.

From this you will get: 4root3/sin 60 = x(AC)/sin 75 ------> eq 1

when you put the value of sins you’ll get:

from this x(AC) will come out to be :

When you compare the value of x to Qty B, you’ll find they both are the same.

hence our answer will be C

Thanks a lot i get it now !

This is never asked in exams by the way so if you ever see a question on those 3rd party test prep. which says you can use some small knowledge of trigonometry to solve this , you should probably skip them . They’re are a waste of your time .

yeah got it mate

No, you actually can solve it. You have to create two triangles, dividing the angle B in a 30 and 45 angle. Thus, you have a 30, 60, 90 triangle on the left, and a 45, 45, 90 triangle on the right. Then you can solve it. There you see that AC (I accidently wrote twice B) is equal to 2 root 2 +2 root 6

Oh so we don’t need trig for this problem. But we do need imagination thanks man