Answer:
3 < x < 7
Step-by-step explanation:
From the diagram; |AB| = |AC|
The length AB is calculated as;
[tex]Sin\ 52^o = \frac{|BD|}{|AB|} \\\\|AB| = \frac{|BD|}{Sin\ 52^o} \\\\|AB| = \frac{12}{Sin\ 52^o} \\\\|AB| =15.228 \ m[/tex]
The length CD is calculated as;
[tex]Sin \ 31^o = \frac{|CD|}{|AC|} \\\\|CD| = |AC| \ \times \ Sin \ 31^o \\\\|CD| = 15.228 \ \times \ 0.515\\\\|CD| = 7.84[/tex]
|CD| = 2x - 6
2x - 6 = 7.84
2x = 7.84 + 6
2x = 13.84
x = 13.84 / 2
x = 6.92
x ≅ 7
Thus, 3 < x < 7
