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

Step-by-step 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=(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=}(1)/(5)rad\cdot r \\ 5=(1)/(5)r \\ to\text{ solve for r} \\ \text{Multiply both sides by 5} \\ 5\cdot5=(1)/(5)r\cdot5 \\ 25=r \end{gathered}`

hence, the answer is

radius=25 feet

x