00:01
We want to find the missing angles of this question, a and c.
00:07
We also want to find the missing side b.
00:10
So we'll start by drawing a diagram using the given information.
00:15
We're told that side a is 78, which of course needs to be directly across from angle a.
00:25
We're told that angle c is 35, which will be.
00:31
Or the side c is 35, which will be directly across from angle c.
00:36
And we are also given angle b, which is 72 degrees, 45 minutes, and we're going to want to find what our side b is.
00:47
In order to find all that missing information, first we need to know what side b is going to be.
00:53
We don't normally do our law of cosines when our angles are written in minutes and degrees, so we're going to start by rewriting our.
01:01
72 degrees as a decimal.
01:04
So we'll take our 72 degrees and we'll add 45 over 60 since it's 45 minutes out of a total of 60.
01:15
That's going to give us 72 plus 0 .75 or 72 .75 degrees.
01:25
Since we are provided two sides and an angle, and we want to find the missing side, we're going to be able to use the law of cosines.
01:41
So to do this, we are going to have, to do this one, we're going to use the formula b squared is equal to a squared plus c squared minus two a.
01:56
C times the cosine of angle b so we'll have b squared is equal to 78 squared plus 35 squared minus 2 times 78 times 35 times the cosine of 72 .75 the last step to that will be to take the square root of both sides, and so we're going to get an approximate answer.
02:32
Since we want this to be rounded to the nearest whole number, after you substitute all of that into your calculator, you're going to get approximately 75.
02:44
So the missing side is 75.
02:51
Next, we want to be able to find our missing angles, a and c...