Answer:
The answer is 6.67 feet, approximately.
Step-by-step explanation:
The image attached shows the context that the problems refered.
Notice that two acute angles from those triangles are congruent, just because their complement are also congruent.
[tex]\angle AOB \cong \angle COD[/tex]
[tex]\angle AOB= \angle COD=90\° - a[/tex]
Remember that the tangent function is defined as
[tex]tan(\theta)=\frac{Opposite \ Leg}{Adjacent \ Leg}[/tex]
Replacing each equiavlence, we have
[tex]tan(90-a)=\frac{6}{4}=\frac{10}{x}[/tex]
Then, we solve for [tex]x[/tex]
[tex]\frac{6}{4} =\frac{10}{x}\\ x=\frac{40}{6}\\ x \approx 6.67 ft[/tex]
Thereofre, the answer is 6.67 feet, approximately.
