Can someone please help solve this question (with a diagram)?

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Answer 1 · 2018-07-04T15:51:21

Law of sines

Law of cossines

#|AB| = x, |AD| = y, angle DAC = alpha#

#angle BAC = 180 - 43 - 72 = 65^0#

#angle BAD = 65^0 - alpha#

#|BD| = |DC| = 4#

#frac{x}{sin 72^0} = 8 / sin 65^0#

#x = 8,395 # cm

#y^2 = x^2 + 4^2 - 2 * x * 4 * cos 43^0#

#y = 6,112# cm

#frac{4}{sin (65^0 - alpha)} = y/sin 43^0#

#sin (65^0 - alpha) = (4 * sin 43^0) / y = 0,44632#

#65^0 - alpha = 26,508#

#alpha = 38,4919 = 38^0 29.5 min#