Question

If the chord of a circle is 24.5 in. long and subtends a central angle of 57.5 degrees what is the radius of the circle?(Do not round until the final answer. Then round to the nearest tenth as needed.)

Answer 1

Okay, here we have this:

Considering the provided information, and the following chord length equation, we obtain the following:

`\begin{gathered} K=2r\cdot sen((\theta)/(2)) \\ 24.5=2r\cdot\text{sen(}(57.5)/(2)\text{)} \end{gathered}`

Now, let's solve for r:

`\begin{gathered} 2r\sin \mleft((57.5^(\circ\:))/(2)\mright)=24.5 \\ r=(24.5)/(2\sin\left(28.75^(\circ\:)\right)) \\ r=25.5\text{ in} \end{gathered}`

Finally we obtain that the radius of the circle is approximately 25.5 inches.