Hello, sinjid9!
A leaning pole is braced at its midpoint as shown.
The pole is 8.2m long and the bracing beam is 6m long.
The foot of the beam is placed 5m from the base of the pole.
Determine to the nearest degree, the angle the pole makes with the ground. Code:
A o
\
\
\ 4.1
\
\
o C
/ \
/ \
6 / \ 4.1
/ \
/ \
D o - - - - - o B
5
The pole is: .$\displaystyle AB = 8.2 \quad\Rightarrow\quad AC = CB = 4.1$
The bracing beam is: .$\displaystyle CD = 6$
We are told that: .$\displaystyle BD = 5$
Law of Cosines: .$\displaystyle \cos B \:=\:\frac{5^2 + 4.1^2 - 6^2}{2(5)(4.1)} \;=\;0.141707317$
Therefore: .$\displaystyle \angle B \;=\;81.85334661 \;\approx\;\boxed{82^o}$