1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trigonometry problem

  1. Oct 7, 2016 #1
    1. The problem statement, all variables and given/known data

    71srah.png

    I don't understand how to get CE.

    2. Relevant equations
    Trigonometric identities (maybe)

    3. The attempt at a solution

    First, I start with the cosine rule
    CB^2 = AC^2 + AB^2 - 2 AC AB cos α
    (CE/sin(β))^2 = (CE/sin(α))^2 + L^2 - 2 (CE/sin(α)) L cos α

    which is gonna be a quadratic equation and it's hard to obtain what CE is (using this method)
    Please help
     
  2. jcsd
  3. Oct 7, 2016 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Try the usual way you derive the cosine rule - except solving for the altitude of the triangle instead of factoring it out.
     
  4. Oct 7, 2016 #3
    I think using sine rule to find a side first is a faster way
     
  5. Oct 7, 2016 #4
    I get this ##(\frac{1}{(sin^2(\beta))})CE^2+(\frac{2\ L\cos \alpha}{sin \ \alpha})CE-L^2=0##

    Then, use the quadratic formula to solve CE??
    But if I use quadratic formula, there will be two solutions, but there is only one CE.
    And I doubt if the solution obtained will be the same as in the photo I gave
     
  6. Oct 7, 2016 #5
    CB/ sin alpha = CA / sin beta

    CE = CA sin alpha
    CE = CB sin beta

    Then whatt??
     
  7. Oct 7, 2016 #6
    angle ACB = 180 - a -b
    you can try to use L/sin(180-a-b) = ??
     
  8. Oct 7, 2016 #7
    Angle ACB = 180 - (a + b)
    sin(180-(a+b)) = sin (a+b)

    L/sin(a+b) = CB/ sin (a) = CA / sin (b)

    Then??
    How to make CE (the altitude) show up o_O?
     
  9. Oct 7, 2016 #8
    You succeeded to express CB (or CA) in terms of L , a and b. Then what is CB sin(b) ?
     
  10. Oct 7, 2016 #9

    L/sin(a+b) = CE/sin(a)Sin(b)
    CE = L sin(a) sin(b)/ sin(a+b)

    Thanks a lot for your help bro
     
  11. Oct 7, 2016 #10

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    ##AE/CE = \cot(\alpha)## and ##BE/CE = \cot(\beta)##. Now add and manipulate.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Trigonometry problem
  1. Trigonometry Problem (Replies: 3)

  2. A trigonometry problem (Replies: 4)

  3. Trigonometry problem (Replies: 22)

  4. Trigonometry problem (Replies: 24)

  5. Trigonometry problem (Replies: 10)

Loading...