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Can you help me please ​

Can you help me please ​-example-1
User Lissette
by
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1 Answer

6 votes

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Answer:

6 < x < 23.206

Explanation:

The smallest that angle CAD can be is 0°. For that, ...

2x - 12 = 0

2x = 12

x = 6

__

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

__

The range of values for x is ...

6 < x < 23.206

_____

Additional comment

You may be expected to assume that angle CAD could be as much as 180°. That cannot be the case.

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