Answer:
w = 13.3, x= 10.3
First option is correct.
Step-by-step explanation:
In triangle ABC, we have
[tex]\tan42^{\circ}=\frac{AB}{BC}\\\\\tan42^{\circ}=\frac{12}{w}\\\\w=\frac{12}{\tan42^{\circ}}\\\\w=13.3[/tex]
Now, in triangle ABD
[tex]\tan27^{\circ}=\frac{AB}{BD}\\\\\tan27^{\circ}=\frac{12}{w+x}\\\\13.3+x=\frac{12}{\tan27^{\circ}}\\\\13.3+x=23.6\\\\x=10.3[/tex]
Thus, we have
w = 13.3, x= 10.3
First option is correct.
