Question

A 30° central angle in a circle is equivalent to π6 radians. Drag a tile to each box to correctly complete the sentence.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The length of the arc intercepted by this central angle is Response area times the length of the Response area.

Answer 1

The length of the arc intercepted by the angle is $\frac{\pi}{6}$ times the length of the radius

Calculating length of an arc

From the question, we are to determine the length of the arc intercepted  by the angle

The length of an arc can be calculated by using the formula,

$l =\frac{\theta}{360 ^\circ} \times 2\pi r$

Where $l$ is the length of the arc

$\theta$ is the central angle

and r is the radius

From the given information,

θ = 30°

∴ $l =\frac{30 ^\circ}{360 ^\circ} \times 2\pi r$

$l = \frac{1}{12}\times 2 \pi r$

$l = \frac{2 \pi}{12}\times r$

$l = \frac{ \pi}{6}\times r$

Hence, the length of the arc intercepted by the angle is $\frac{\pi}{6}$ times the length of the radius

Learn more on Calculating length of an arc here: https://brainly.com/question/10824096

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