00:02
In trial abc, we have the information.
00:05
Ad is an angle bisector, meaning the angle is bisected.
00:10
So i'd like to find, first find this angle a, and then we can bisect it.
00:14
We can do this with law of signs.
00:17
The law of signs would say side a, which is opposite angle a squared, would be equal to the sum of the squares of the other two sides, minus two times the product of the other two sides, times the cosine of the included angle.
00:30
And then we can subtract 16 squared, subtract 24 squared, divide by negative 2 times 16 times 24, and then take the inverse cosine of that, and we'll have angle a.
00:50
So a calculator like decimals, just make sure it's in degree mode to begin, and then the inverse cosine of 19 squared minus 16 squared, minus 24 squared over negative 2 times 16 times 24 is about 52 degrees and so if we go back to that angle by sector that would put about 26 degrees on each side.
01:40
Now we can find if that's angle or if that's point d we could next want to ultimately find a d so i'm going to use the law of signs now and say that the sign of the whole angle a of 52 degrees over its opposite side 19 is equal to the sign i want to find angle b sign of angle b over 24 cross multiply the 24 and then inverse sign and we have angle b so the inverse sign of 24 sine 52 over 19 is about 84 .5 degrees and so if we subtract from 180 180 the 84 .5 minus the 52 will give us 43 .5 degrees for angle c.
03:05
Now we can find a d and then we'll be able to find the area of each triangle.
03:14
So to find ad we could also use the law of signs.
03:17
We can say that the sign of angle b over its opposite side ad is equal to actually we don't have enough information for that yet.
03:33
Not the way i was going to set it up.
03:35
Let me complete the smaller triangles.
03:39
180 minus 84 .5 minus 26.
03:44
Would give 69 .5 degrees here...