WEBVTT
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Probably the most familiar equation or formula for finding an area of a triangle is 1/2 the base times the
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height, but you may not know the base and the height of a triangle. But in trig, we have some other formulas,
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and one that we can use is if you know two sides and an included angle you can use one of these formulas
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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.
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You can see that this is a and c and beta, so that's your two sides and the included angle. So the area,
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very easy to calculate, is 1/2 times 5 times 8 times the sine of 10 degrees. So let's see what that is.
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That's going to be approximately 3.47 units squared, whatever your units would be.
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That's how you can find the area of a triangle, very simply, if you know two sides and an included angle.
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If you know the measurement of three sides of a triangle, you can use a formula called Heron's formula.
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It takes a little bit of calculation, but it's not difficult to use. First you find a value, s, that's the semiperimeter.
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It's the sum of the three sides divided by two, and then it's just a matter of substituting these values into
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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.
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Now again, and you could do this probably in your head, but you know if the numbers are kind of large or
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you've got some decimals, just make sure you remember to put parentheses around your numerator, and
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then you'll be all right and get the right answer. Another thing you might want to do if you know how to
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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
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as a variable. So if I store x, or store it as you know that variable, then when you enter this in your calculator
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you don't have to keep writing this over and over again, entering this, you can just use those values.
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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
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to write all this out... minus 50 and... Now, it's an easy formula to use, but since there are so many calculations
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in there you just have to be careful because you could definitely make a little calculation error and get the
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wrong answer. So you want to maybe double check your answers when you do this, and you want to put
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parentheses into your square root in your calculator. You want to make sure you put parentheses around
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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
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your variable, like I said, then it'll be a lot easier to enter. So that's going to be approximately
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1815.46 square units, and that's how you can find the area of a triangle if you know all three sides.