Math

An isosceles triangle has an area of 24 cm squared, and the angle between the two equal sides is 5 pi/6. What is the length of the two equal sides? I can't figure out how to set up this problem please help! Thank you!

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  1. draw altitude from angle between equal sides to base (hits at pi/2 because sides equal)
    angle there is half angle = 5 pi/12 which is 75 deg
    call altitude h , base of whole triangle is b so our right triangle has base b/2
    then
    h tan 75 = b/2
    A = 24 = hb/2 = 24 = h^2 tan 75
    h^2 = 24/tan 75
    h = 2.5359
    then
    L = h/cos 75
    L = 9.798

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