Can this Secant-Tangent Equation be Simplified Further?

  • Thread starter Cyclopse
  • Start date
  • Tags
    Simplifying
In summary, the student was trying to solve for AC and was not successful. They suggested drawing a radius from O to B and using the Pythagorean Theorem to find r.
  • #1
Cyclopse
10
0

Homework Statement


Is it possible to simplify this even further?
28b4d3b.jpg


Homework Equations


This is a Secant-tangent equation.
Secant: AD = 18/radical 3 AC = ??

The Attempt at a Solution


I cross multiplied to get 18=324radical 3 (AC)
and in the end i got 0 = (18radical3) (AC) which makes no sense

so is there a different way to simplify that?
 
Physics news on Phys.org
  • #2
Cyclopse said:

Homework Statement


Is it possible to simplify this even further?
28b4d3b.jpg


Homework Equations


This is a Secant-tangent equation.
Secant: AD = 18/radical 3 AC = ??

The Attempt at a Solution


I cross multiplied to get 18=324radical 3 (AC)
Are you trying to solve for AC?
Cyclopse said:
and in the end i got 0 = (18radical3) (AC) which makes no sense
When you divide both sides by 18, you will be left with 1 on the left side, not 0.

If you are trying to find AC, divide both sides by 324√3.
Cyclopse said:
so is there a different way to simplify that?
 
  • #3
Mark44 said:
Are you trying to solve for AC?

Yes.
Here is the original question
dh09i.jpg
 
Last edited:
  • #4
It doesn't seem to me that you have enough information.

How did you go from AB = 18 and AD = 18/√3 to 18 = 324√3 * AC?
 
  • #5
Mark44 said:
It doesn't seem to me that you have enough information.

How did you go from AB = 18 and AD = 18/√3 to 18 = 324√3 * AC?

I'm really terrible at maths...that's why I'm here.
 
  • #6
Draw a radius from O to B, and call its length r. The radius OB is perpendicular to AB, so that ABO is a right triangle.

Let θ = the angle at A.

Then, from your given information,

cos(θ) = 18/(r + 18/√3), and
sin(θ) = r/(r + 18/√3)

Now you have two equations in two unknowns, so you should be able to solve for both unknowns, although you only need r. Once you know r, it's pretty easy to get AC.
 
Last edited:
  • #7
Start out like Mark44 said by drawing a radius from O to B, and call its length r, but then apply the Pythagorean Theorem to the right triangle ABO to find r.

Chet
 
  • #8
Chestermiller said:
Start out like Mark44 said by drawing a radius from O to B, and call its length r, but then apply the Pythagorean Theorem to the right triangle ABO to find r.
That's simpler than what I suggested. Simple is good!
 

1. How do I simplify an equation?

Simplifying an equation involves combining like terms and using algebraic rules to reduce the equation to its simplest form.

2. What are some common techniques for simplifying equations?

Some common techniques for simplifying equations include distributing, factoring, and canceling out common factors.

3. Can I use different techniques to simplify an equation?

Yes, there are often multiple ways to simplify an equation, so you can choose the technique that is most comfortable for you or most effective for the equation at hand.

4. Why is it important to simplify equations?

Simplifying equations can make them easier to solve or understand, and can also help identify patterns or relationships between variables.

5. Are there any tips for simplifying complex equations?

One tip is to break down the equation into smaller parts and simplify each part individually before combining them back together. Also, keep an eye out for common factors or terms that can be simplified or canceled out.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
3
Views
2K
  • Precalculus Mathematics Homework Help
Replies
3
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
9
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
220
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
  • Precalculus Mathematics Homework Help
Replies
8
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
2K
  • Precalculus Mathematics Homework Help
Replies
10
Views
2K
Back
Top