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Math Help - [SOLVED] Finding Area of a Scalene Triangle

  1. #1
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    [SOLVED] Finding Area of a Scalene Triangle

    A scalaene triangle has 3 sides: RS = 12.1, ST = 19.8, RT = 17.4. NOw i have to find the area of the triangle.
    It didn't say which side was the base, so I made side ST the base. Then, I made a dotted line for the height, H. So now there's 2 triangles: RSY, and RYT. Triangle RSY has RS which is 12.1, and angle Y, which is 90 degrees. How can I figure out other information for triangle RSY with only that info? I thought i'd use trigonometric ratios. So, the sin of Y = o/h = i'm not sure. the hypotenous is 12.1, but what is the opposite side for angle Y, which is a right angle?
    Sorry, I know this post must seem rambling.... but thats what progress I've made on the qu., lol. I would appreciate any help you may have. I know, I'm not asking for the answer. I just need some step-by-step instructions to guide me though. thank you.
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  2. #2
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    Quote Originally Posted by ria3 View Post
    A scalaene triangle has 3 sides: RS = 12.1, ST = 19.8, RT = 17.4. .
    Heron's formula!

    RonL
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  3. #3
    Behold, the power of SARDINES!
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    Law of Cosines

    Quote Originally Posted by ria3 View Post
    A scalaene triangle has 3 sides: RS = 12.1, ST = 19.8, RT = 17.4. NOw i have to find the area of the triangle.
    It didn't say which side was the base, so I made side ST the base. Then, I made a dotted line for the height, H. So now there's 2 triangles: RSY, and RYT. Triangle RSY has RS which is 12.1, and angle Y, which is 90 degrees. How can I figure out other information for triangle RSY with only that info? I thought i'd use trigonometric ratios. So, the sin of Y = o/h = i'm not sure. the hypotenous is 12.1, but what is the opposite side for angle Y, which is a right angle?
    Sorry, I know this post must seem rambling.... but thats what progress I've made on the qu., lol. I would appreciate any help you may have. I know, I'm not asking for the answer. I just need some step-by-step instructions to guide me though. thank you.
    [SOLVED] Finding Area of a Scalene Triangle-capture.jpg

     \cos^{-1}\alpha=1.056<br />

    So you end up with

     \frac{1}{2}19.8(12.1)\sin(1.056) \approx 104.3
    Last edited by TheEmptySet; March 18th 2008 at 07:55 AM. Reason: I took the arcsine for some unknow reason sorry :(
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  4. #4
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    Hello, ria3!

    A scalaene triangle has sides: RS = 12.1,\;ST = 19.8,\; RT = 17.4
    Find the area of the triangle.

    Someone will mention Heron's Formula . . . which is the fastest method.
    But, assuming you know Trigonometry, I'll show you another way . . .

    We have: . \Delta RST with angles R,S,T
    . . and their respective opposite sides: r=19.8,\;s=17,4,\;t=12.1

    The area of the triangle is: . A \;=\;\frac{1}{2}rs\sin T
    . .
    (One-half the product of two sides times the sine of the included angle.)


    To find \angle T, we use a variation of the Law of Cosines: . \cos T \;=\;\frac{r^2 + s^2 - t^2}{2rs}

    We have: . \cos T \;=\;\frac{19.8^2 + 17.4^2 - 12.1^2}{2(19.8)(17,4)} \;=\;0.795875421

    . . Then: . T \:\approx\:37.3^o


    Hence: . A \;=\;\frac{1}{2}rs\sin T \;=\;\frac{1}{2}(19.8)(17.4)\sin37.3^o \;=\;104.2918726

    . . Therefore: . A \;\approx\;104.3\text{ units}^2

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  5. #5
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    Thanks EmptySet! I have a qu. about how you did it though:
    you did:
    h=12.1 sin (2)
    h = 12.1 sin(0.514)
    How did you get sin2? In the triangle you drew, you wrote something for one of the angles, but i can't make out what number it is.
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  6. #6
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    Thanks Soroban! When finding cosT, can I use the cosine law (instead of the variation, cuz i think that's what is expected of me)? i did, and I got
    cosT = 25.4167.
    cos 25.4167 = 0.9032
    so angle T = 25 degrees... which is very different from your answer. i'm not sure why i'm getting a different answer?
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  7. #7
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    never mind those 2 qu., lol.
    i've got it!!
    thank you guys soo much!!!
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