Question

S denotes the length of the arc of a circle of radius r sub tended by the central angle 0. Find the missing quantity. 0=1/5 radian, s=5 feet, r=?

Answer 1

25 feet

Explanation

Step 1

the length of arc is given by:

$\begin{gathered} S=\emptyset\cdot\text{ r} \\ where\text{ }\emptyset\text{ is the angle in radians} \\ \text{and r is the radius} \end{gathered}$

then, Let

$\begin{gathered} \emptyset=\frac{1}{5}radians \\ s=5\text{ ft} \\ r=r(\text{unknown value)} \end{gathered}$

replace

$\begin{gathered} S=\emptyset\cdot\text{ r} \\ 5\text{ ft=}\frac{1}{5}rad\cdot r \\ 5=\frac{1}{5}r \\ to\text{ solve for r} \\ \text{Multiply both sides by 5} \\ 5\cdot5=\frac{1}{5}r\cdot5 \\ 25=r \end{gathered}$

hence, the answer is

radius=25 feet

x