Answer:
Option C. [tex]x=(8)tan(50\°)[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC
The tangent of 40 degrees is equal to divide the opposite side to angle of 40 degrees (AB) by the adjacent side to angle of 40 degrees (BC)
[tex]tan(40\°)=\frac{AB}{BC}[/tex]
substitute the given values
[tex]tan(40\°)=\frac{8}{x}[/tex]
Solve for x
[tex]x=\frac{8}{tan(40\°)}[/tex]
Remember that
m∠A+m∠C=90° ----> by complementary angles
we have
m∠C=40°
therefore
m∠A=50°
The tangent of 50 degrees is equal to divide the opposite side to angle of 50 degrees (BC) by the adjacent side to angle of 50 degrees (AB)
[tex]tan(50\°)=\frac{BC}{AB}[/tex]
substitute the given values
[tex]tan(50\°)=\frac{x}{8}[/tex]
Solve for x
[tex]x=(8)tan(50\°)[/tex]
