Student+Workpage+-+Sample

= Proving the Law of Cosines = Name: _ __Date:__ __

media type="custom" key="6409689" Procedure


 * STEP 1:** Break the triangle above into 2 triangles. The triangle on the right will be labeled BDC and the triangle on the left will be labeled BDA. Draw those triangles with their respective side lengths below (notice that side **//h//** is common between both triangles).

media type="custom" key="6409703"


 * STEP 2:** For triangle BDC, what is the cosine of angle **C**? Write this expression in terms of side **x**.




 * STEP 3:** Restate the Pythagorean Theorem in terms of the sides of triangle BDC. Rearrange this equation so that it is in terms of **h2**.


 * STEP 4:** Restate the Pythagorean Theorem in terms of the sides of triangle BDA. Write this equation in terms of **c2**. Expand any binomials and simplify the expression.


 * STEP 5:** Substitute the equation for **h2** from question 3 into the equation for **c2** from question 4.


 * STEP 6:** Substitute the equation for **x** from question 1 in to the equation resulting from question 5.

Questions


 * Question 1:** Does your final equation from step 6 look familiar?


 * Question 2:** What have we just done?


 * Question 3:** How would you modify the procedure in this worksheet to show that this works for any other side in a given triangle ABC?