The quadrilateral ABCD in the figure has AB = 4, AD = 4.5, CD = 5, angle ABC = 100°
and angle BCA = 30°.
what is the size of angle D?

Question

The quadrilateral ABCD in the figure has AB = 4, AD = 4.5, CD = 5, angle ABC = 100° 
and angle BCA = 30°. 
 what is the size of angle D?

anonymous · Answer

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anonymous · Answer

well here you can use sine and cosine laws to find out stuff

anonymous · Answer

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anonymous · Answer

sorry just forgot to add that in. so now we use sine law to find length of AC. so

anonymous · Answer

sinA/a = sinB/b
sin30/4 = sin100/AC

anonymous · Answer

ACsin30=4sin100
AC=4sin100/sin30
AC=-2.025/-0.988
AC=2.05 units

anonymous · Answer

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anonymous · Answer

now we have have 2 triangles: the top one and the bottom one. we need the angle in the bottom one. now for the bottom triangle, we know 3 sides but no angles so here we use cosine law.

anonymous · Answer

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anonymous · Answer

and you solve it. unfortunately when i finished, my angle was wrong and i have no time to re do it but good luck, i assure you that the process is right