Answer:
![\theta=0.45rad](https://img.qammunity.org/2021/formulas/mathematics/middle-school/kqxij3d4nfp823hhemak8yzeqwxyqou5qd.png)
Explanation:
The radian measure of the centeral angle of a circle of radius r and arc length of s, can be calculated using the relation:
![s=r\theta](https://img.qammunity.org/2021/formulas/mathematics/college/ooo4k9liwszkoqp8szrdayaq488xwqrxjw.png)
The radius is given as
and the arc length is given as:
![s=10ft](https://img.qammunity.org/2021/formulas/mathematics/middle-school/qdf08o8bsuryk3y4iq9q01a33nr30i0z78.png)
Let us substitute the values into the formula and solve for
.
This implies that:
![10=22\theta](https://img.qammunity.org/2021/formulas/mathematics/middle-school/v6kjjk7vdq9ud8vbyz7ex8ieh2d1sp0y83.png)
We divide both sides by 22
![(10)/(22)=\theta](https://img.qammunity.org/2021/formulas/mathematics/middle-school/6sissqpc88xd9c5a5tujdnumag2i7v0t74.png)
Therefore
![\theta=(5)/(11)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/j8i84zj6a0hrxogj2mjmux91jwntv23e8z.png)