Page 107 - IM_FL_Geometry_Print Sample

Student Task Statement
Here is a circle with a central angle that measures 40 degrees that encloses an arc of length cm.
1. What is the radius of the circle?
2. What is the radian measure of ?
Student Response
1. 13.5 cm.
2. radians or equivalent.
Student Lesson Summary
We de ned the radian measure of an angle by drawing an arc on that angle and then taking the ratio of the arc length to the radius for that arc. Using symbols, if the central angle of the arc is radians, the radius is units, and the arc length is units, then we can write
We can also use this de nition to nd the length of an arc if we know its radius and radian angle measure:
For example, suppose we had an arc with radius 3 which had a central angle that measured radians. This would mean that the ratio of its arc length to its radius was equal to , and
34
Teacher Guide