Answer:
The value of x=4 meters.
Step-by-step explanation:
Let DC=x m
In triangle ABC
\(\theta=35.5{\circ}\)
AB=10 m
We know that
\(tan\theta=\frac{perpendicular side }{Base}\)
\(tan35.5^{\circ}=\frac{AB}{BC}\)
\(0.713=\frac{10}{BC}\)
\(BC=\frac{10}{0.713}\)
BC=14.02m
In triangle EBD
EB=14 m
\(\theta=54.5^{\circ}\)
\(tan54.5=\frac{EB}{BD}\)
\(1.4019=\frac{14}{BD}\)
\(BD=\frac{14}{1.4019}\)
BD=9.98 m.
BC=BD+DC
14.02=9.98+x
By using substituting property
x=14.02-9.98
By using subtraction property of equality
x=4.04
x=4 ( nearest meter)
The value of x=4 m.
