We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
74
2
avatar

Find \(AC\).

 

https://latex.artofproblemsolving.com/9/1/d/91d520533f0fb8cb325932013b2aebf0db9bde54.png

 May 28, 2019
 #1
avatar
0

The answer is 2 root 3

 May 28, 2019
 #2
avatar+102434 
+1

We can use the Law of Cosines

 

BC^2  = AC^2 + AB^2 - 2(AC)(AB)cos(BAC)

 

(7√3)^2  = AC^2 + 9^2 - 2(AC) (9) (-√3/2)

 

147  = AC^2 + 81 + 9√3AC  subtract 81 from both sides

 

66 = AC^2 + 9√3AC

 

AC^2 + 9√3AC - 66 = 0        let  AC = x

 

x^2 + 9√3x - 66 = 0

 

Using the quadratic formula

 

-9√3 + √[ (9√3)^2 + 4*66]            -9√3 + √[169 *3 ]        -9√3 + 13√3                4√3

____________________    =  _______________  =   ____________  =       ____  =

             2                                           2                                 2                             2

 

 2√3  =  x  = AC

 

cool cool cool

 May 28, 2019

15 Online Users