# Law of Cosines: Discovery

- Author:
- Tim Brzezinski

- Topic:
- Cosine, Trigonometry

Interact with the applet below for a few minutes.
Then, answer the questions that follow.

(Be sure the black slider has been slid all the way to the right before answering these questions.)

## 1)

Write an equation that expresses the relationship among *A, x, *and *b*.
Then, if necessary, rewrite this equation so that *x* is written in terms of *b* and *A*.

## 2)

Write an equation that expresses the relationship among *b*, *x*, and *h*.

## 3)

Without introducing a new variable, write an equation that expresses the relationship among the sides of Triangle *BDC*.

## 4)

Rewrite the equation you wrote in response to question (3) so that each side of the equation is written in simplest form.

## 5)

Now use any one (or more) equations you've written in response to the questions above **so that the equation you wrote for (4) contains no power of x and no power of h. **