Chord Radius Degree calc: radius is known, AB is also known

[Snupple]

Hoping someone can help me with this

AB is known (eg 150)
Radius is also known (eg 600)

How can I work out the (black) arc knowing these two numbers?

Cheers

 

[Deleted member 4993]

View attachment 7897
Hoping someone can help me with this

AB is known (eg 150)
Radius is also known (eg 600)

How can I work out the (black) arc knowing these two numbers?

Cheers

I am assuming you know Sine, Cosine and Tangent functions.
Drop a perpendicular from the center of the circle to AB. It will bisect AB. Now think in terms of Cosine function and continue.....

 

[HallsofIvy]

You can do it directly using the "cosine law". If triangle ABC has sides a, b, and c, each opposite the angle with the same letter, then \(\displaystyle c^2= a^2+ b^2- 2ab cos(C)\). Here, we can take a= b= 600 and c= 150 so the equation becomes \(\displaystyle 150^2= 600^2+ 600^2- 2(600)(600)cos(C)\) or \(\displaystyle 22500= 7200- 720000 cos(C)\).

 

[Snupple]

Isn't the Law of Sines simpler?

r = radius, c = chord AB
central angle = 2 * ASIN[c / (2r)]

Superb - that worked... thanks for _all_ the replies