WEBVTT
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at the area of a triangle. And I know
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you have learned how to do area of a triangle
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usually using a equals one half the base times height
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. However, in this lesson, we're gonna be
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looking at the area of a triangle using the trigonometry
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functions sine cosine tangent. We're gonna focus, really
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? On sign on this one, though. There's
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a couple of different ways you can find it.
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But when you have what we're gonna follow this rule
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for finding the area of a triangle. The area
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of a triangle is the product of the length of
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two sides is the product of I'm sorry. It's
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product of half the length of two sides and there
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sign of their included angle. So what we would
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do if we were finding area that we could do
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a different ways. It kind of depends on what
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information you're given. So to find the area you
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could if you're gonna use sign of a, you
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would use half of length be and late, see
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times sign of A. If you're gonna use sign
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of B, you're going to use half of a
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Tom C. Tom Sana be. And if you're
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going to use. See angle. See, it's
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gonna be half of a Tom's be sign of C
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. So depending on which angle you're given will depend
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on which side you're gonna want to use. But
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you're gonna follow the same process. So if I'm
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giving angle A I'm gonna use besides B and C
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to find my area. If I'm giving angle,
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see, I'm gonna use sides A and C.
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I'm sorry, A and B, I'm gonna use
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the opposite sides. And if I'm giving angle B
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, I'll use a and sit. So let's look
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at a couple of examples. Let's start with this
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one where we have a triangle where Ace side length
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of a s, five side length of CS six
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and angle B is 112 degrees. Well, in
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this one, I'm given Angle Bay. So this
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means that I'm going to use Side A and Side
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B course. I'm giving those sides so I can
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find the area. So to use an angle,
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a I mean angle be your area would be one
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half of a Tom's See son, Be so for
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this one, the substitute her numbers in place of
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our angles and sides. So we'd have half of
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a We've got five, and for see we have
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six and sign of 112 degrees. Well, we
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can go ahead and multiply one half times five times
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six is 30 Tom sign of 112 degrees and half
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of 30th 15. So we're really finding 15 times
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. Sign off 112 degrees and you'll definitely need to
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use your calculator on this one. So if I'm
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going to approximate, I'm gonna go ahead for this
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purpose. I'm going around it right now to 0.92
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seven and 15 times. 0.9 to 7 is approximately
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13.9 and we're going around these to the nearest 10th
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. So in the area of my triangle is approximately
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13.9 units squared. So let's look at another one
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. This one. They didn't give us the actual
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triangle assed faras a picture, but they did give
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us our information. They told us that angle A
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is 31 degrees. Side B is 18 and side
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see is 22. This is all the information we
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need to find the area of this triangle. Since
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we're given angle A, we're gonna be used.
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Binding Sign of a. So that means that our
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area, we're going to use the formula one half
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of be Tom C son of angle A. So
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in this case, that's gonna be half of 18
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times 22 sign of 31 18 times 22 is 396
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and half of that is 198. So when around
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that I would have 198 and then sign a 31
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I'm gonna have approximately 0.515 And that's going to give
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me an approximate area of 101 point. Not so
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All you're gonna do to kind of review is your
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whatever angle you're given, you're gonna use the two
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opposite sides because those were going to be the adjacent
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sides to that angle. You're gonna use those two
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leaks to find the area of the triangle