Can someone help me
Question
2 Answer

1. User Answers sqdancefan
Answer:
6 < x < 23.206
Stepbystep explanation:
To properly answer this question, we need to make the assumption that angle DAC is nonnegative and that angle BCA is acute.
The maximum value of the angle DAC can be shown to occur when points B, C, and D are on a circle centered at A*. When that is the case, the sine of half of angle DAC is equal to 16/22 times the sine of half of angle BAC. That is, ...
(2x 12)/2 = arcsin(16/22×sin(24°))
x ≈ 23.206°
Of course, the minimum value of angle DAC is 0°, so the minimum value of x is ...
2x 12 = 0
x 6 = 0 . . . . . divide by 2
x = 6 . . . . . . . add 6
Then the range of values of x will be ...
6 < x < 23.206
_____
* One way to do this is to make use of the law of cosines:
22² = AB² + AC² 2·AB·AC·cos(48°)
16² = AD² + AC² 2·AD·AC·cos(2x12)
The trick is to maximize x while satisfying the constraints that all of the lengths are positive. This will happen when AB=AC=AD, in which case the equations be come ...
22² = 2·AB²·(1cos(48°))
16² = 2·AB²·(1 cos(2x12))
The value of AB drops out of the ratio of these equations, and the result for x is as above.

2. User Answers Lexiooooooo
Answer 6<x<30:
Stepbystep explanation: