Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

Math question?

Segments AB and BC in the triangle below are congruent and angle B measures 37°. Given that the area of the triangle is 22, find the length of segment AC.

2 Answers

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  • 2 months ago

    Since AB = BC = y ( suppose ) , Angle C = Angle A

    Let AC  =  x.

    Area  of Triangle ABC  =  (1/2) AC * y sin (71.5)  =  22

    => (1/2) x * sin (71.5) y  = 22

    => x y  =  22 * 2 / sin (71.5) = 46.3977  ............ (1)

    From sine rule --

    x / (sin 37)  =  y/sin 71.5

    . . . . .. . y * ( sin 37)

    => x  = ------------------ =   y * 0.6346 ........... (2)

    .   .   .   .  sin 71.5 

    From (1) and (2)

    .. . . . . 46.3977 * 0.6346

     x  =  --------------------------

     . . . . . . . . .   x

    x²  =  27.4443

    =>  x  =   5.426 .............................. Answer

    Attachment image
  • Sean
    Lv 5
    2 months ago

    AB = BC = u

    by area formulas

    .5*sin 37 * u^2 = 22

    u^2 = 44/sin 37 = 73.11

    AC/2 = u*sin 37/2 (in triangle APC p the perpendicular)

    AC = 2*u*sin(37/2) = 5.426

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