Enter the data in the table above into your grapher or computer. Create a scatter plot

Chapter 5, Problem 467

(choose chapter or problem)

The ratio (sin A)/a that shows up in the Law of Sines shows up another way in the geometry of \(\triangle A B C\): It is the reciprocal of the radius of the circumscribed circle.

(a) Let \(\triangle A B C\) be circumscribed as shown in the diagram, and construct diameter \(C A^{\prime}\). Explain why \(\angle A^{\prime} B C\) is a right angle.

(b) Explain why \(\angle A^{\prime}\) and \(\angle A\) are congruent.

(c) If a, b, and c are the sides opposite angles A, B, and C as usual, explain why \(\sin A^{\prime}=a / d\), where d is the diameter of the circle.

(d) Finally, explain why (sin A)/a = 1/d.

(e) Do (sin B)/b and (sin C)/c also equal 1/d? Why?

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back