Hi. This is my question:
An art student wants to make a string collage by connecting six equally spaced points on the circumference of a circle to its center with string. What would be the radian measure of the angle between two adjacent pieces of string, in simplest form?
This is a math b regents practice tests question, and I have no idea how to solve it. Please help me! Thank You!
Since all 6 points on the circumference of the circle are equally spaced, the string running from each outer point to, and around the center point, and back to the next outer point forms 6 equilateral triangles. The 6 angles formed by the radial strings from the center to the outer points sum to 360º making the central angle of each triangle 60º. By definition therefore, the remaining two angles within each triangle must total 120º making the two outer angles of each triangle 60º each.
The angles between adjacent outer string sides of the hexagon are therefore 120º apart.
To find the radian measure of the angle between two adjacent pieces of string, we need to determine the angle formed at the center of the circle.
Since there are six equally spaced points on the circumference connected to the center, the circle can be divided into six equal parts. Each part represents the central angle between two adjacent points on the circumference.
To find the radian measure of this angle, we can use the formula for finding the central angle in a regular polygon:
Central angle = (360 degrees) / (number of sides)
In this case, the number of sides is 6, so let's plug it into the formula:
Central angle = (360 degrees) / (6)
Central angle = 60 degrees
To convert degrees to radians, we use the conversion factor: π radians = 180 degrees
By substituting the values into the formula, we can calculate the angle in radians:
Central angle in radians = (60 degrees) * (π radians / 180 degrees)
Central angle in radians = (60π) / 180
Simplifying the expression by canceling out 60 from both numerator and denominator, we get:
Central angle in radians = π / 3
So, the radian measure of the angle between two adjacent pieces of string is π/3 or 1/3π (in simplest form).
Of course! I'll be happy to help you solve this question.
To find the radian measure of the angle between two adjacent pieces of string, we need to first find the central angle between two adjacent points on the circumference of the circle.
Given that there are six equally spaced points on the circumference of the circle, we can calculate the central angle using the formula:
Central Angle = 2π / Number of Points
In this case, the number of points is 6, so the formula becomes:
Central Angle = 2π / 6
Simplifying this equation gives us:
Central Angle = π / 3
Therefore, the radian measure of the angle between two adjacent pieces of the string is π/3 (in simplest form).
Um... I think its 60* ... I think if not, sorry
360*/6=60*