Quick and explain how to do ths problem

Choice D) 8.5 ft

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Refer to the image attachment

Step 1) Find angle ACB

tan(angle ACB) = AB/AC
tan(angle ACB) = 21/57
angle ACB = arctan(21/57)
angle ACB = 20.224859

Step 2)  Use the result of step 1 to find the angle ACD

angle ACD = angle ACB + angle DCB
angle ACD = 20.224859 + 7.1
angle ACD = 27.324859

Step 3) Now use this angle, with the tangent rule, to find the length AD

tan(angle ACD) = AD/AC
tan(27.324859) = (21+x)/57
0.516688 = (21+x)/57
0.516688*57 = 21+x
29.451216 = 21+x
29.451216-21 = 21+x-21
8.451216 = x
x = 8.451216
x = 8.5

Edit: Sorry nearly forgot about the attachment. My bad

The answer would be d i think but i’m for sure it is not a and c