A little trig

  1. this is a question that was part of an mcq test.
    and i did'nt have any clue as to how to begin!
    finally i just tried plugging in values for A,B,C to see if they worked.
    for ex. i put A=B=C=60 (degrees)- equilateral and so on..but i'd like to know the logical way to do it...

    if A,B,C are the vertices of a triangle,
    and if cosBcosC + sinAsinBsinC = 1

    is the triangle
    a) equilateral
    b) isosceles
    c) right angled isosceles
    d) right angled but not isosceles
    e) none of the above.
     
  2. jcsd
  3. Right, I'm assuming you know sin^2 +cos^2 = 1.

    Well you can see this is nearly similar, and almost exactly the same if B = C. So there's two angles the same.

    So now cos^2 + sinA sin^2 = 1

    Which means sinA must be 1.

    Therefore A can only take value of 90 degrees - right angle (450...etc useless here)

    180 - 90..other two angles combine as total 90 degrees, so they must be 45 each since you've already found they're the same. Which leaves you a right angled isosceles.
     
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