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anonymous

  • one year ago

Solve for the missing length and the other two angles in the triangle below. I will add an attachment! Thank you!

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    @zepdrix

  3. anonymous
    • one year ago
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    @mathmate could you help please?

  4. mathmate
    • one year ago
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    Typically, when two sides of a triangle and the included angle is known, you can use the cosine rule to find the third side, and then sine rule to find the remaining angles.

  5. anonymous
    • one year ago
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    Okay the cosine rule is a^2=b^2+c^2-2bc cosA So if I plug that in i get a^2=4^2+3^2-2(4)(3) cos(15 degrees) a^2 is approximately 1.8 sqrt 1.8 = aproximately 1.35 Is that right??

  6. mathmate
    • one year ago
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    Yes, 1.348251 to be closer, but yes, 1.35 is correct!

  7. anonymous
    • one year ago
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    Thank you! I have another question that is similar to this but the cosine rule does not work. I am supposed to find length a.

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  8. mathmate
    • one year ago
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    However, you need more figures to do the sine rule calculations, or else you angles will be off!

  9. anonymous
    • one year ago
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    For my first question. To find the angles would I set up ratios? If so, i got 1.8/ sin(15)= 4/ sin b Then i would cross multiply??

  10. mathmate
    • one year ago
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    Exactly, but 1.348/sin(15)...

  11. anonymous
    • one year ago
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    oh yeah. how about my second problem?

  12. mathmate
    • one year ago
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    The same strategy for the second problem, since two sides and included angle are known. The fact that 108 > 90 degrees does not matter, because cos108 will then be negative, and everything will work out.

  13. anonymous
    • one year ago
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    So use the cosine rule?

  14. mathmate
    • one year ago
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    Yep, cosine rule, followed by sine rule (whenever 2 sides and included angle are known).

  15. anonymous
    • one year ago
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    I get: a^2=13^2+11^2-2(13)(11) cos(106) but when i plug this in i get- 368.32 and the square root it and get: 19.205 is that right?

  16. mathmate
    • one year ago
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    I get 19.4520 , you can double check my number. Sorry, gtg.

  17. anonymous
    • one year ago
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    I still get 19.205 but thank you!

  18. mathmate
    • one year ago
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    I think the angle is 108, unless I made a mistake. @haileycaroen

  19. mathmate
    • one year ago
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    I think the angle is 108, unless I made a mistake. @HaileyJCaroen

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