geometry question

Question

Part of a school’s stage is shaped like a sector of a circle, as shown below. The students do not yet know the exact dimensions of this part of the stage, but they want to identify as many relationships as possible so that they will be able to decorate this part of the stage when the dimensions are available.

 

 

The length of s is 12 feet, and the length of a is 10 feet. Determine the measure of ∠1 in both degrees and radians.

Answer 1

If a central angle θ in a circle with radius r intercept an arc on the circle of length s, then the arc length s is given by s=r θ where θ is in radians or s=r θ(π/180) where θ is in degrees.

In you case: 12= 10 θ therefore θ = 12/10 =1.2 radians.

You can either transform 1.2 radians in degree or use second formula to find your angle in degrees.