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

• Mar 9th 2013, 02:50 PM
aioria1995
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!!!
• Mar 9th 2013, 07:15 PM
Soroban
Re: Diagram and Trig/Pre-Calc prob... really confusing...
Hello, aioria1995!

Did you make a sketch?

Quote:

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
$\displaystyle 75^2 \:=\:20^2 + 50^2 - 2(20)(50)\cos D \quad\Rightarrow\quad 5625 \:=\:2900 - 2000\cos D$

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

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

The witness' description is impossible.

Quote:

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