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!!!

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