Im struggling with this arc length problem, please help!

[cleanthony99]

Ill post question by question to make it easy to understand. I need help on number three and four but 1 and 2 help with those.

1. Have each group member measure the arc on the side of the snowboard and the chord length for the snowboard.
Arc Length= 120.4cm Chord Length= 120 cm

2. If tis board is said to have an 8.57cm meter radius side cut, find the angle measure (in radians) that was cut out.
.14 Radians

3. Measure the chord length for this board. If the chord length has to be this long on another board, but the board has an 8 meter radius side cut, find the angle measure in radians, that was cut out of that board.

4. Using the radian measure found in step 3, find the arc length of the new board.


I know it has somehting to do with s=r theta but im extremely confused. Please help! Thanks in advance!

 

[DrPhil]

Ill post question by question to make it easy to understand. I need help on number three and four but 1 and 2 help with those.

1. Have each group member measure the arc on the side of the snowboard and the chord length for the snowboard.
Arc Length= 120.4cm Chord Length= 120 cm

2. If tis board is said to have an 8.57cm meter radius side cut, find the angle measure (in radians) that was cut out.
.14 Radians

3. Measure the chord length for this board. If the chord length has to be this long on another board, but the board has an 8 meter radius side cut, find the angle measure in radians, that was cut out of that board.

4. Using the radian measure found in step 3, find the arc length of the new board.


I know it has somehting to do with s=r theta but im extremely confused. Please help! Thanks in advance!

You need to know (or to find) the relationship between chord length and arc length of a sector of a circle, as a function of the radius of the circle. When you shorten the radius but keep the same chord length, the depth of the will be greater and hence the arc length will be greater.

Draw the picture with three radial lines from the center of the circle to the two ends and the midpoint of the cut. The midline is perpendicular to the chord, making two similar right triangles. If the full angle is theta, then
arc length = r*theta

Looking at either of the triangles, with hypotenuse r, short leg (chord/2), and vertex angle (theta/2),
chord length = 2*(r sin(theta/2))

ok?