 Hello friends, so here is a question on similar triangles. Let's try and solve this it's given that there are two triangles and Sides have been given a b as you can see 3.8 bc is 6 centimeter C a is 3 root 3 centimeter and Ed is 6 to 3 e f is 12 and bf is 7.6 and We have to find out The angle f Okay, angle f. So Let's try and do this some so in triangle ABC so let's consider these two triangles in triangles ABC and triangle You can take any points right now and we'll see later on it looks like D F e Are going to be the order of the points, but anyways, so let's say in triangle ABC and DFE What do we see? So you can check a b By let's find out a b upon FD So a b upon FD or DF It's better to write Df here So, let me write Df. Yep. So a b by Df a b upon Df is how much a b is 3.8 centimeter and What about Df Df is 7.6 isn't it? So that means this is how much this will be one upon two a b by Df is one upon two Also, let's find out BC by F e BC by F e again, if you see this is 6 centimeter By 12 centimeter, which is equal to one upon two again So it gives us a hint that it is going to be a similar triangle pair Not but then just to confirm. Let's do CA upon Ed Okay, CA Upon Ed and how much is that CA is as you can see in the figure here three root three so three root three centimeter divided by six root three centimeter and Again, this is one upon two So what do we conclude? a b by Df is equal to BC By F e is equal to CA by Ed Is it CA by Ed therefore by By SS SS similarity criteria similarity Criterion We can say what can be said guys that triangle a b c is Similar to triangle now the correspondence is very important, right? So corresponding point to a is D clearly and corresponding point to B is F and To see is E. So these are the two similar triangles Okay, and now I'm going to write it here Okay, so therefore Therefore Angle F is clearly equal to angle C I'm sorry angle F. No, so angle F is not B. Sorry angle F is angle B. Sorry Angle F is Angle B Angle B an angle B from this figure is 60 degrees So angle F is equal to 60 degrees Correct So this is how we established and what did we do in this problem? Basically, so we first of all established that all the ratios are equal Okay, and once the side ratios are equal then clearly the Two triangles are similar. Hence the individual corresponding angle pair will be equal So that's how we found out angle F is 60 degrees. I hope You understood this problem