WEBVTT

00:00:07.105 --> 00:00:13.606
Probably the most familiar equation or formula for finding an area of a triangle is 1/2 the base times the

00:00:13.608 --> 00:00:19.601
height, but you may not know the base and the height of a triangle. But in trig, we have some other formulas,

00:00:19.603 --> 00:00:25.605
and one that we can use is if you know two sides and an included angle you can use one of these formulas 

00:00:25.607 --> 00:00:34.102
to find the area of a triangle. So let's look at an example there. Suppose we have a is 5, c is 8, and beta is 10. 

00:00:34.104 --> 00:00:43.851
You can see that this is a and c and beta, so that's your two sides and the included angle. So the area, 

00:00:43.853 --> 00:01:02.850
very easy to calculate, is 1/2 times 5 times 8 times the sine of 10 degrees. So let's see what that is. 

00:01:02.852 --> 00:01:17.852
That's going to be approximately 3.47 units squared, whatever your units would be. 

00:01:17.854 --> 00:01:23.598
That's how you can find the area of a triangle, very simply, if you know two sides and an included angle.

00:01:26.340 --> 00:01:32.853
If you know the measurement of three sides of a triangle, you can use a formula called Heron's formula.

00:01:32.855 --> 00:01:39.603
It takes a little bit of calculation, but it's not difficult to use. First you find a value, s, that's the semiperimeter.

00:01:39.605 --> 00:01:46.808
It's the sum of the three sides divided by two, and then it's just a matter of substituting these values into

00:01:46.810 --> 00:02:01.321
the square root and calculating it. So let's see what we get here. We have s is 100 plus 50 plus 75 divided by 2. 

00:02:01.323 --> 00:02:06.576
Now again, and you could do this probably in your head, but you know if the numbers are kind of large or 

00:02:06.578 --> 00:02:13.840
you've got some decimals, just make sure you remember to put parentheses around your numerator, and 

00:02:13.842 --> 00:02:18.839
then you'll be all right and get the right answer. Another thing you might want to do if you know how to 

00:02:18.841 --> 00:02:25.840
do it, and it's a good thing to learn how to do, is to store this value as x in your calculator. You can store it 

00:02:25.842 --> 00:02:31.851
as a variable. So if I store x, or store it as you know that variable, then when you enter this in your calculator

00:02:31.853 --> 00:02:36.106
you don't have to keep writing this over and over again, entering this, you can just use those values. 

00:02:36.108 --> 00:02:48.371
Alright, so A, the area rather, capital A, is going to be [the square root of] s. This is going to take a little while

00:02:48.373 --> 00:03:05.872
to write all this out... minus 50 and... Now, it's an easy formula to use, but since there are so many calculations

00:03:05.874 --> 00:03:11.619
in there you just have to be careful because you could definitely make a little calculation error and get the

00:03:11.621 --> 00:03:15.870
wrong answer. So you want to maybe double check your answers when you do this, and you want to put 

00:03:15.872 --> 00:03:20.648
parentheses into your square root in your calculator. You want to make sure you put parentheses around

00:03:20.650 --> 00:03:33.165
the whole thing so that you don't mess up on that. So let's see. So that's...and if you've put the value of s into 

00:03:33.167 --> 00:03:42.675
your variable, like I said, then it'll be a lot easier to enter. So that's going to be approximately 

00:03:42.677 --> 00:03:59.426
1815.46 square units, and that's how you can find the area of a triangle if you know all three sides.