1. ## find theta

find theta without the use of the law of cosines

see image attached

2. Originally Posted by calc123
find theta without the use of the law of cosines

see image attached
Why can't you use the Cosine Rule?

3. well my prof told me i didnt need to know that for the test. so im trying to solve it a diff way

4. Hello, calc123!

Find $\theta$ without the use of the Law of Cosines.
Code:
      |     x     A
D + - - - - - o
|         **
|     5 * *
y |     *  *
| θ *   *
| *    *
B o     * 7
|    *
|   *
3 |  *
| *
|*
C o

We have: . $AB = 5,\;\;BC = 3,\;\;AC = 7$

Let: . $AD = x,\;\;BD = y,\;\;\theta = \angle DBA$

$\begin{array}{ccc}\text{In right triangle }ADB\!: & x^2+y^2 \:=\:5^2 & [1] \\ \\

\text{In right triangle }ADC\!: & x^2 + (y+3)^2 \:=\:7^2 & [2] \end{array}$

Subtract [2] - [1]: . $(y+3)^2 - y^2 \:=\:49 - 25 \quad\Rightarrow\quad 6y \:=\:15 \quad\Rightarrow\quad y \:=\:\frac{5}{2}$

Hence: . $\cos\theta \:=\:\frac{\frac{5}{2}}{5} \:=\:\frac{1}{2}$

Therefore: . $\theta \;=\;\frac{\pi}{3}\;\;(60^o)$