The arc length is s=rθ, where r is the radius=10cm, and θ is the subtended angle. Therefore θ=s/10 radians.

The chord length L forms the base of an isosceles triangle with vertex angle θ. We can split the triangle using the perpendicular bisector from the vertex to the base. We now have two congruent right triangles with hypotenuses length r=10 and vertex angle ½θ=s/20. Using trigonometry we have ½L/10=sin½θ=sin(s/20).

So L=20sin(s/20) cm.

- All categories
- Pre-Algebra Answers 12,296
- Algebra 1 Answers 25,199
- Algebra 2 Answers 10,412
- Geometry Answers 5,147
- Trigonometry Answers 2,633
- Calculus Answers 5,956
- Statistics Answers 3,013
- Word Problem Answers 10,014
- Other Math Topics 6,543

81,213 questions

85,312 answers

2,153 comments

68,747 users