Answer
$32^{\circ}$.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the cycles turning radius be $R$.
Because the angle $B$ varies inversely as $r$ we have:
$\Rightarrow B=\frac{k}{R}$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $R=4\; feet$ and $B=28^{\circ}$.
Substitute into the equation (1).
$\Rightarrow B=\frac{k}{R}$
$\Rightarrow 28=\frac{k}{4}$
Multiply both sides by $4$.
$\Rightarrow 4\cdot 28=4\cdot \frac{k}{4}$
Simplify.
$\Rightarrow 112=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=112$ into the equation (1).
$\Rightarrow B=\frac{112}{R}$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $R=3.5\; feet$ into the equation (2).
$\Rightarrow B=\frac{112}{3.5}$
Simplify.
$\Rightarrow B=32$
Hence, the banking angle is $32^{\circ}$.
