0

I'm trying to calculate the radius for the following problem based on the intersection of the blue and red lines (length and angle)

enter image description here

I tried simple trigonometry to calculate half the length of the chord = 150mm

enter image description here

But not sure how to calculate the sagitta which i could then use to calculate the radius as per Sagitta - The height of an arc or segment

Any suggestions?

Carlos
  • 103

1 Answers1

2

You can mark radius $=r$. Making a triangle from the centre to the end of the blue line, we can use the law of cosines: $$ r² = (770-r)^2 + 238^2 - 2\times 238 \times (770-r) \cos{141} $$ from which we solve $r \approx 489.23$

enter image description here

Steven Alexis Gregory
  • 26,769
Matti P.
  • 6,012
  • Thanks to both @steven gregory and @Matti P.for the answer

    The following is the equation solved for r

    r = (x^2 + y^2 - 2 * y * x * cos(a)) / 2*(x - y * cos(a)

    x = 770 y = 238 a = 141 r = 489.23

     – Carlos Apr 13 '18 at 10:22