PLEASE HELP WILL MARK BRAINLIEST

Apply the sine theorem in triangle ABC:

sin C = AB/AC = 4/5

=> C  = arcsin(4/5) = 53.13 deg

As shown in picture, AB//CD. Using the same side interior angles theorem:

=> angle BCD = angle ABC = 90 deg

=> angle ACD = 90 - angle ACB = 90 - C = 90 - 53.13 = 36.87 deg

Apply the cosine theorem in triangle ACD:

cos C = AC/CD

=> CD = AC/cos C = 5/cos(36.87) = 5/0.8 = 6.25

=> Option C is correct

Hope this helps!

:)

step-by-step explanation:

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