00:01
In the first question, we have this figure abcd made out of five equilateral triangles.
00:08
So you can see that their length are all the same.
00:15
Now, i'm going to name the side of an equilateral triangle as 2x.
00:22
So it means this portion here will just be x.
00:29
Now, we want to find the angle between ac and ad.
00:32
So it will be like this, this angle here.
00:37
So i'm just going to drop down a right angle triangle here.
00:42
Now this is the midpoint, since this is equilateral triangle, this will be the midpoint.
00:47
So distance here will be x and this part here will be x.
00:54
So this distance here is 5x.
01:00
Now how about the heights here? i'll name it h.
01:06
So just looking at this triangle here, this is h, and here is x.
01:21
Now how do we find h? now, if this side is 2x, this will be 2x as well, because it's equilateral triangle.
01:39
So by pythagoras theorem, h is square root of 2x square minus x square.
01:49
And so i'll get square root of 3x square, and that would be square root 3x.
01:58
X.
02:01
So my h is square root 3x.
02:07
Now since i have two sides now i can find the angle here.
02:12
So angle tangent of angle c a d is equals to opposite over adjacent.
02:23
So that would be root 3x over 5x.
02:28
The x cancels off.
02:30
So angle cad is tangent inverse root 3 over 5...