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anonymous

  • one year ago

Suppose angle a=pi/6 radians and length of b=5

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  1. anonymous
    • one year ago
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  2. mathstudent55
    • one year ago
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    There are 3 angles in your triangle. One measures pi/3. Another angle is a right angle. You can calculate the measure of the third angle.

  3. anonymous
    • one year ago
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    so angle A=30 degrees, and angle b=60 degrees

  4. mathstudent55
    • one year ago
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    What is the sum of the measures of the angles of a triangle?

  5. anonymous
    • one year ago
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    the sum is 180 degrees.. got that down :) I'm just having trouble with finding the lengths.

  6. mathstudent55
    • one year ago
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    Angle A does not measure 30 deg. Also, they want the answer in radians.

  7. hartnn
    • one year ago
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    she has done similar problems before :) what have you tried for a and c ?

  8. anonymous
    • one year ago
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    if you convert 30 degrees into radians you get pi/6

  9. anonymous
    • one year ago
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    sin30=5/c, c*sin30=5,c=5/sin30, 5 divided by 1/2, = 5*2 which is 10

  10. hartnn
    • one year ago
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    sin 30 = 5/c sure?? B is 60 degrees

  11. anonymous
    • one year ago
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    oops that's the cosine

  12. mathstudent55
    • one year ago
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    Yes, you are correct. I was thinking of angle B, which is the one they are asking for. 180 deg = pi rad The sum of the measures of the angles of a triangle is 180 deg = pi rad. m<A + m<B + 90 = 180 m<A + m<B + pi/2 = pi pi/6 + m<B + pi/2 = pi pi/6 + m<B + 3pi/6 = 6pi/6 m<B = 2pi/6 m<B = pi/3

  13. mathstudent55
    • one year ago
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    Now let's look at finding the length of a.

  14. hartnn
    • one year ago
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    yea, now try again

  15. hartnn
    • one year ago
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    math, she is faster than you think ;)

  16. anonymous
    • one year ago
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    :) cosine 30=5/c

  17. anonymous
    • one year ago
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    we know that cosine is sqrt3/2

  18. mathstudent55
    • one year ago
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    |dw:1443985244529:dw|

  19. hartnn
    • one year ago
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    good! so c = ... ?

  20. anonymous
    • one year ago
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    c=10/sqrt(3)?

  21. mathstudent55
    • one year ago
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    |dw:1443985322492:dw|

  22. hartnn
    • one year ago
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    yessss! now onto a

  23. anonymous
    • one year ago
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    we can use tan30=a/5

  24. hartnn
    • one year ago
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    so a =... ?

  25. anonymous
    • one year ago
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    well we know that tan 30=sqrt(3)/3

  26. hartnn
    • one year ago
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    sqrt 3/ 3 = 1/sqrt 3

  27. anonymous
    • one year ago
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    5sqrt(3)/3?

  28. hartnn
    • one year ago
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    yes, correct! 5 (sqrt 3)/3 or 5/ sqrt 3

  29. hartnn
    • one year ago
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    one good way to verify, side opposite to 30 degree angle should come out to be half the hypotenuse :)

  30. mathstudent55
    • one year ago
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    We know the measure of angle A and the length of the adjacent side, b. We want the length of the opposite side, a. The tangent function relates the lengths of the opposite and adjacent sides: \(\tan A = \dfrac{opp}{adj} \) \(\tan \dfrac{\pi}{6} = \dfrac{a}{5}\) \(a = 5 \tan \frac{\pi}{6} \) \(a = \dfrac{5 \sqrt{3}}{3} \)

  31. mathstudent55
    • one year ago
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    \(\sin A = \dfrac{opp}{hyp}\) \(\sin \dfrac{\pi}{6} = \dfrac{\frac{5\sqrt{3}}{3}}{c}\) \(\dfrac{1}{2} = \dfrac{\frac{5\sqrt{3}}{3}}{c}\) \(c = \dfrac{10\sqrt{3}}{3}\)

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