testing header
Math Goodies is a free math help portal for students, teachers, and parents.
Free Math
Newsletter
 
 
Interactive Math Goodies Software

Buy Math Goodies Software
testing left nav
Math Forums @ Math Goodies
Math Forums @ Math Goodies
Home | Profile | Active Topics | Members | Search | FAQ
Username:
Password:
Save Password
Forgot your Password?

 All Forums
 Homework Help Forums
 Geometry and Trigonometry
 OK with tan but ...
 New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic  

daimath
Junior Member

USA
6 Posts

Posted - 07/13/2013 :  02:28:37  Show Profile  Reply with Quote
Start with a triangle ABC with angle ACB =
Then length AB = tan x length AC

So far so good.

But assume that C is at the center of a circle with a radius of AC and that line AD is drawn so that D is at the intersection of line BC and the circumference of the circle.

How does one calculate the length of AD by reference to the length of AC and the angle ?

(It would have been nice to have been able to add a diagram to illustrate the problem but I can't see how to do that.)
Go to Top of Page

daimath
Junior Member

USA
6 Posts

Posted - 07/13/2013 :  20:17:11  Show Profile  Reply with Quote
Sorry! I should have made it clear that triangle ABC is a right angled triangle with the lines AB and AC subtending the right angle.
Go to Top of Page

Ultraglide
Advanced Member

Canada
299 Posts

Posted - 07/13/2013 :  23:59:59  Show Profile  Reply with Quote
I will make one assumption - the point D is not on the same side of AB as the centre C. Note that DC is a radius and is equal to AC and is the angle between DC and AC. Using the Law of Cosines, cos = (DC+AC-AD)/(2DC.AC). Rearranging, AD = DC + AC - 2DC.ACcos. Since AC=DC. AD = 2AC- 2ACcos which gives:

AD = AC(2(1-cos)
Go to Top of Page

daimath
Junior Member

USA
6 Posts

Posted - 07/14/2013 :  06:23:22  Show Profile  Reply with Quote
Thanks Ultraglide. Your answer is much appreciated.
Go to Top of Page
  Previous Topic Topic Next Topic  
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
Math Forums @ Math Goodies © 2000-2004 Snitz Communications Go To Top Of Page
This page was generated in 0.04 seconds. Snitz Forums 2000
testing footer
About Us | Contact Us | Advertise with Us | Facebook | Blog | Recommend This Page




Copyright © 1998-2014 Mrs. Glosser's Math Goodies. All Rights Reserved.

A Hotchalk/Glam Partner Site - Last Modified 21 Nov 2014