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Answer:
6 < x < 23.206
Step-by-step explanation:
The smallest that angle CAD can be is 0°. For that, ...
2x - 12 = 0
2x = 12
x = 6
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The largest angle CAD can be is the angle that corresponds with triangle CAB being isosceles: CA = AB = AD. Then the length of AC satisfies ...
AC·sin(48°/2) = 22/2
On the other side, we have ...
AC·sin((2x-12)/2) = 16/2
This gives us ...
sin(x -6) = 8/11·sin(24°)
x = 6 + arcsin(8/11·sin(24°)) ≈ 23.206
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The range of values for x is ...
6 < x < 23.206
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Additional comment
You may be expected to assume that angle CAD could be as much as 180°. That cannot be the case.
