trigonometry

posted by .

Use logarithms and the law of tangents to solve the triangle ABC, given that a=21.46 ft, b=46.28 ft, and C=32°28'30"

Also Give checks.

I know the use of logarithms is unnecessary but i have to show my solution by using logarithms and that's the only reason I'm asking for help. Logarithms confuse me. Please help me.

  • trigonometry -

    If you are not already familiar with the law of tangents, here's an article that can help you:

    http://en.wikipedia.org/wiki/Law_of_tangents

    We will be using the same notations in the following solution.

    In the given case, sides a,b are known, and the included angle C. So the sum of angles
    A+B=180-C = 180 - 32-28-30 = 147-31-30 = 1967π/2400 radians
    a+b=21.46+46.28=67.74
    a-b=21.46-46.28=-24.82

    By the law of tangents,
    tan(A-B)/tan(A+B)=(a-b)/(a+b)
    or
    tan(A-B)=tan(A+B)(a-b)/(a+b)
    =0.2331984

    In log (to base 10), cannot calculate the values of negative numbers, so we will keep track of the sign ourselves:
    log(-tan(A+B)) = -0.1962309
    log(-(a-b)) = 1.394801777162711
    log(a+b) = 1.830845192308612
    log(tan(A+B)*(a-b)/(a+b) = -0.1962309+1.3948018-1.8308452
    =-0.6322743
    Antilog(-0.6322743)=0.2331985 as before.
    Convert 0.2331985 to degrees,
    A-B=13-21-41, and
    A+B=147-31-30
    A = (160-53-11)/2=80-26-36
    B = (134-09-49)/2=67-04-55
    side c can be found by the cosine rule or the sine rule.
    Check my work.

  • trigonometry - correction -

    Anon & Drws, thank you for pointing out there is a problem with this solution.

    The tangent rule formula that I used was not correct. The formula used for the tangent rule is simply:
    (a-b)/(a+b) = tan((A-B)/2)/tan((A+B)/2)

    Using the previous values,
    a=21.46
    b=46.28
    C=32-28-30=32.475
    We have
    A+B=180-32.475=147.525
    a+b=67.74
    a-b=-24.82

    Now apply the tangent rule:
    tan((A+B)/2)=3.433633
    tan((A-B)/2)=tan((A+B)/2)*(a-b)/(a+b)
    = -1.2580863
    (A-B)/2 = atan(1.2580863)= -51.520285
    A-B = -103.04057

    A=(147.525-103.04057)/2=22.242215°
    B=(147.525+103.04057)/2=125.282785°

    c can be found by the sine rule or the cosine rule, since 5 of the six unknowns have been calculated. I get c=30.44083 using the cosine rule and it checks with the sine rule.

    I believe you can now handle the logarithm part. If you need further help, just post.

    I apologize again for the unforgivable mistake in applying the tangent rule formula.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    use the power law of logarithms to verify the product law of logarithms for log10^2
  2. trigonometry

    okay so i have this trigonometry problem were i HAVE to use logarithms. Now this is my work but can u help me solve it using logarithms. Find the area of the following triangles:(use logarithms) 1) c=426, A=45degrees 48' 36",and B=61degrees …
  3. trigonometry

    1. Finde the area of the following tringles: (use Logarithms) A) a=12.7, b=21.5, c=28.6. i'm not of the answer i got. i got 127.6 if you got something different can you show me how you did while using logarithms.
  4. trigonometry (MathMate)

    MathMate i would really appreciate if you can show me where the logarithms can be used.I know they are unnecessary and I already found the answer without them but i still have to show my work using logarithms and they just confuse …
  5. Trigonometry (Logarthims)

    Give checks to the following two questions Use logarithms and the law of tangents to solve the triangle ABC, given that a=21.46 ft, b=46.28 ft, and C=32°28'30" without logarithms i can do this problem easily and i have. but when i …
  6. trigonometry (repost) Mathmate

    I want to start by saying thank you . You have no idea how much u have helped me understand logarithms, even better then the books i have (it poorly explains the subject of trigonometry let alone logarithms and antilog). Your last …
  7. trigonometry

    Use logarithms and the law of tangents to solve the triangle ABC, given that a=21.46 ft, b=46.28 ft, and C=32°28'30" I have to use logarithms and law of tangents . and then provide the check. which says law of sine or mollweids equation. …
  8. trigonometry (repost) Mathmate

    Use logarithms and the law of tangents to solve the triangle ABC, given that a=21.46 ft, b=46.28 ft, and C=32°28'30" Using the previous values, a=21.46 b=46.28 C=32-28-30=32.475 We have A+B=180-32.475=147.525 a+b=67.74 a-b=-24.82 …
  9. kahyla

    use the properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. show your work Ln 8x 2. log2y^5
  10. pre calculous

    use the properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. show your work ln x^2/y^3 Assuming x,y AND z are positive use properties of logariths to write the expression …

More Similar Questions