# find theta

• Apr 25th 2010, 06:16 AM
calc123
find theta
find theta without the use of the law of cosines

see image attached
• Apr 25th 2010, 06:18 AM
Prove It
Quote:

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?
• Apr 25th 2010, 06:29 AM
calc123
well my prof told me i didnt need to know that for the test. so im trying to solve it a diff way
• Apr 25th 2010, 07:27 AM
Soroban
Hello, calc123!

Quote:

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