Option C: [tex]12\sqrt{2} \ ft[/tex] is the length of BC
Explanation:
Given that the triangle ABC
The length of [tex]AC=12 \ ft[/tex], [tex]m\angle B=45^{\circ}[/tex]
We need to determine the length of BC
Length of BC:
The length of BC can be determined using the trigonometric ratios.
[tex]sin \theta=\frac{opp}{hyp}[/tex]
Substituting [tex]\theta=45[/tex] , [tex]Opp=BC=12[/tex] and [tex]hyp=BC[/tex], we get,
[tex]sin \ 45=\frac{12}{BC}[/tex]
[tex]BC=\frac{12}{sin \ 45}[/tex]
Simplifying the values, we get,
[tex]BC=\frac{12}{\frac{1}{\sqrt{2}}}[/tex]
Dividing, we get,
[tex]BC=12\sqrt{2}[/tex]
Thus, the value of BC is [tex]12\sqrt{2} \ ft[/tex]
Hence, Option C is the correct answer.
