Calculate radius with part chord

Question

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

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

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?

Answer 1

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 $r \approx 489.23$