Question

Determine the arc length of IJ.
Round your answer to two decimal places.

Answer 1

The approximate value of the arc length between the hour hand and the minute hand of a clock showing 10:00 a.m. is 12 meters.

Step-by-step explanation:

The arc length between the hour hand and the minute hand of a clock can be calculated using the formula:

arc length = radius * angle

In this case, the radius of the clock is 0.2 m and the angle between the hour hand and the minute hand at 10:00 a.m. is 60 degrees (since each hour mark on the clock represents 30 degrees).

Therefore, the arc length can be calculated as:

arc length = 0.2 m * 60 degrees = 12 m

So, the approximate value of the arc length is 12 meters.

Answer 2

From the picture, we can tell that arc IJ has a central angle of 160° and that the circle has a diameter of 14 cm, or a radius of 7 cm.

Remember that the formula for arc length is:

`L = r\theta`

• 
  `r` is the radius of the arc
• 
  `\theta` is the central angle (in radians)

We are almost able to find the arc length, but 160° is not in radians, which it has to be in order for us to properly use the formula. In order to convert it to radians, multiply the degree measure by
`(\pi)/(180)`.

`160^(\circ) = 160 \cdot (\pi)/(180)`

`160^(\circ) = (8\pi)/(9)`

Now, we can use the formula:

`L = 7 \cdot (8\pi)/(9) = (56\pi)/(9) \approx 19.55`

The answer is approximately 19.55.