# Thread: Diagram and Trig/Pre-Calc prob... really confusing...

1. ## Diagram and Trig/Pre-Calc prob... really confusing...

At a criminal trial, the witness gave the following testimony: "the defendant was 20 ft from the victim. I was 50 ft from the defendant and 75 ft from the victim when the shooting occurred, I saw the whole thing."
a) Use the law of cosines to show that the testimony has errors.
b) How else could you know that the testimony has errors?

Thanks!!!

2. ## Re: Diagram and Trig/Pre-Calc prob... really confusing...

Hello, aioria1995!

Did you make a sketch?

At a criminal trial, the witness gave the following testimony:
"The defendant was 20 ft from the victim.
I was 50 ft from the defendant and 75 ft from the victim when the shooting occurred."

a) Use the Law of Cosines to show that the testimony has errors.
Code:
              20
D o  *  *  *  *  *  o V
*              *
*           *
50 *        * 75
*     *
*  *
o
W
$75^2 \:=\:20^2 + 50^2 - 2(20)(50)\cos D \quad\Rightarrow\quad 5625 \:=\:2900 - 2000\cos D$

$2000\cos D \:=\:-2725 \quad\Rightarrow\quad \cos D \:=\:-\frac{2725}{2000} \:=\:-1.3625$

But $\cos D$ must be betweeen $\text{-}1$ and $+1$

The witness' description is impossible.

b) How else could you know that the testimony has errors?
Lengths of 20, 50, and 75 cannot form a triangle.
Code:
              *       *
20 *             *    50
*                   *
*                         *
*   *   *   *   *   *   *   *   *
75