1. Not finding help here? Sign up for a free 30min 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!

Finding angle of a reflected isosceles triangle

  1. Sep 25, 2012 #1
    1. The problem statement, all variables and given/known data
    I am trying to find the following (marked in red) angle, I know that the radii to the points of contact make an angle θ with the horizontal.

    2me5pw0.jpg


    2. Relevant equations
    all angles of a triangle add up to 180 degrees.
    isosceles triangle, has two equivalent sides


    3. The attempt at a solution
    5l0yv8.png

    I tried using symmetry and found the part in red is [itex]\pi[/itex] - 2[itex]\theta[/itex]
    but according to the text, the angle is 2[itex]\theta[/itex]. I am confused on why is is 2[itex]\theta[/itex]
     
  2. jcsd
  3. Sep 25, 2012 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    The sides of the inverted triangle are tangents to each circle.
    The base of your blue triangle is 2R.
    The angles on either side of the base must be ##\theta##.

    The blue-triangle apex angle must be ##\pi-2\theta## ... which is where you've got up to.

    The apex of the blue triangle forms a diamond shape with the inverted triangle.
    The bottom of the diamond is the angle you want.
    The left-hand angle is the same as the right-hand angle - you actually know what these angles are!

    What do the angles in the diamond add up to?
    What do the left hand and right hand angles add up to?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Finding angle of a reflected isosceles triangle
Loading...