# Trig help

#### 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 agree, the angle the pole makes with the ground.

#### monster

Assuming i understand the questions (As shown is tough when not shown) you have a triangle with bottom 5 and opposite side 6 and you want to find the angle made with the ground,

Well,

tan $$\displaystyle \theta$$ = opposite / adjacent

therefore,

tan $$\displaystyle \theta$$ = 6/5

so,
$$\displaystyle \theta$$ = tan-1 (6/5)

hence, $$\displaystyle \theta$$ = 50.19 degrees

#### Soroban

MHF Hall of Honor
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: .$$\displaystyle \angle B \;=\;81.85334661 \;\approx\;\boxed{82^o}$$