00:01
We now determine the missing parts of this triangle a, b, c.
00:04
Here we are given the two angles of the triangle, that is angle a equals 51 degree, angle c equals 42 degree, and we are also given one of the side lengths, that is the side length c is given as 14.
00:18
And we have to determine the angle b, the side length a, and then the side length b.
00:23
First, let's determine this angle b.
00:26
And for that, observe that since we know two angles of the three angles of the.
00:30
The triangle we can use the angle some property of a triangle to determine the angle b and according to the angle some property of triangle the sum of the interior angles of triangle equals 180 degree and that means if we add up the three angles that is angle a plus angle b plus angle c of the triangle abc this equals 180 degree we already know angle a and angle c so i'm going to replace angle a by 51 degree and we write angle b plus angle c which is given as 42 degree and this equals 180 degree.
01:33
Now we add these two angles.
01:36
51 degree plus 42 degree that is 93 degree and this added with angle b equals 180 degree.
01:48
So solving for angle b.
01:49
We get angle b and this equals 180 degree minus 93 degree.
01:56
We subtract 93 degree from both sides.
01:59
And so this equals 87 degree.
02:04
Thus we determine angle b and that equals 87 degree.
02:10
So here we write angle b equals 87 degree.
02:17
Now let's determine the side length of this triangle.
02:22
And for that i'm going to use the side.
02:24
Here i use this form of the sign law that is the side length a over sign of angle a and this equals side length let's use side length see because we know that so this is side length the c over sign of angle c you basically use this form of sign law now let's put the value of the angle a, angle c as well as the side length of c.
03:00
Since we do not know the side length a, we write this as a, and this over sign of angle a, that is a sign of 20 degree.
03:09
And this equals, we know the value of side length c, that is 14, and this is over sign of angle c, and that is sine 42d.
03:18
Now we can solve for the side length a from this equation.
03:24
First i cross multiply like this and i do that i get a times of sine 42 degree and this equals 14 times of sine 51 degree...