00:01
So in this question, the three given points are the vertices of a triangle.
00:04
I want to solve the triangle rounding the length of the sides to the nearest tenth and the angle measures to the nearest degree.
00:12
So let's see here.
00:14
I have a, b, and c.
00:17
A is the point zero, zero.
00:22
B is the point four, negative three.
00:28
And c is the point one, negative five.
00:38
And so here is my triangle.
00:42
So let's figure out our side lengths first.
00:46
So let's get side ab.
00:48
To find side ab, i use the distance formula.
00:53
I'm getting the square root of x2 minus x1 being squared, 4 minus 0 being squared, plus y2 minus y1 being squared, plus negative 3 minus 0 being squared.
01:11
That's the square to 16 plus 9, square to 25, my ab is 5.
01:22
Now, let's get a c.
01:27
Again, i'll use the distance formula.
01:30
The square root of 1 minus 0 being squared, plus y2 minus y1 being squared, negative 5 minus 0 being squared.
01:44
Squared of 1 plus 25, this is the square root of 26.
01:54
Okay, so this guy here is the square root of 26.
01:59
And they said round that to the nearest 10th.
02:03
If you head to a calculator, the square of 26 is 5 .1.
02:09
So your ac here to the nearest 10th is 5 .1.
02:18
And then i need b .c.
02:21
So b .c, again, i'm going to use the distance formula.
02:27
I get the square root of 4 minus 1 being squared, plus negative 3.
02:39
Minus negative 5 being squared.
02:46
That looks like the square root of 3 squared plus negative 3 plus 5, that's 2 squared.
02:56
Squared of 9 plus 4, square to 13.
03:03
And if i round to the nearest 10th, my squareer to 13, that ends up being 3 .6.
03:13
So if you head to your calculator, you'll see that your bc is 3 .6.
03:20
Now, we need to get our angles.
03:24
So this, i'm going to use my law of cosines.
03:28
Okay.
03:30
And i will find first, i'll find angle b.
03:35
It doesn't really matter.
03:37
Okay.
03:38
How can i find angle b? well, if i want to get angle b, what can i say? i can say that the cosine of angle b is equal to little a squared plus little c squared, minus little b squared over 2 a c my little a is across from angle a that's the square to 13 being squared plus my little c my little c is across from angle c that's 5 in my little b that's across from angle b that's the square to 26 being squared over two times a square to 13 times 5...