Question

explore radian measure by following these steps.

1. move point l to set arc length t equal to arc length s.
2. move point m to set arc length u equal to the other two arc lengths.
3. what is best estimate for the number of radians in one half circle?

m∠jok = 1.00 radian
m∠kol = 1.00 radian
m∠lom = 1.00 radian
u = 10.0
t = 10.0
s = 10.0
r = 1

Explanation:

Step1: Recall the definition of radian

A radian is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. For a circle with radius \( r \), the circumference is \( C = 2\pi r \), and a half - circle (semicircle) has an arc length of \( \pi r \).

Step2: Relate arc length and radians for a half - circle

We know that the formula for the length of an arc \( s \) in terms of the radius \( r \) and the central angle \( \theta \) (in radians) is \( s=r\theta \). For a half - circle, the arc length \( s = \pi r \) (since the length of a semicircle is half of the circumference \( 2\pi r\)). Substituting into the arc - length formula \( s = r\theta \), we get \( \pi r=r\theta \). Dividing both sides by \( r \) (assuming \( r
eq0 \)), we find that \( \theta=\pi\approx3.14 \). But from the given diagram, we can also think in terms of the number of 1 - radian angles that fit into a half - circle. Since \( \pi\approx3 \) (as a rough estimate from the options given: 1, 2, 3), and we know that the exact value of the number of radians in a half - circle is \( \pi\approx3 \).

Answer:

3