+0  
 
0
416
3
avatar

ABCD is a rhombus. If PB=12, AB=15, and m<ABD=24, find each measure

Heres the problem:

Thanks for your help!

Guest Apr 5, 2015

Best Answer 

 #1
avatar+80956 
+10

23.  Using the Law of Cosines, we have

AP^2  = 15^2 + 12^2  - 2(15)(12)cos 24

AP = about 6.33

 

24. The diagonals of a rhombus bisect each other, therefore AP = PC  = 6.33

 

25. Since the diagonals bisect each other, BP = PD = 12. So, BD =24. And we can use the Law of Cosines to find AD

AD^2  = 24^2 + 15^2 - 2(24)(15)cos 24

AD  = about 11.97

So, using the Law of Sines

sin BDA / AB = sin 24 / AD

sinBDA / 15 = sin 24 / 11.97

sin-1(15 sin 24 / 11.97) = BDA = 30.64°

 

26. We can use the Law of Cosines to find ACB....note BC = AD = 11.97  and AC = 2(AP) =2(6.33) = 12.66

AB^2 = BC^2 + AC^2 - 2 - 2(BC)(AC)cosACB

15^2 = 11.97^2 + 12.66^2 - 2(11.97)(12.66)cosACB

cos-1 = (15^2 - 11.97^2 - 12.66^2) / (-2(11.97)(12.66)) = ACB = 74.98°

 

  

CPhill  Apr 5, 2015
Sort: 

3+0 Answers

 #1
avatar+80956 
+10
Best Answer

23.  Using the Law of Cosines, we have

AP^2  = 15^2 + 12^2  - 2(15)(12)cos 24

AP = about 6.33

 

24. The diagonals of a rhombus bisect each other, therefore AP = PC  = 6.33

 

25. Since the diagonals bisect each other, BP = PD = 12. So, BD =24. And we can use the Law of Cosines to find AD

AD^2  = 24^2 + 15^2 - 2(24)(15)cos 24

AD  = about 11.97

So, using the Law of Sines

sin BDA / AB = sin 24 / AD

sinBDA / 15 = sin 24 / 11.97

sin-1(15 sin 24 / 11.97) = BDA = 30.64°

 

26. We can use the Law of Cosines to find ACB....note BC = AD = 11.97  and AC = 2(AP) =2(6.33) = 12.66

AB^2 = BC^2 + AC^2 - 2 - 2(BC)(AC)cosACB

15^2 = 11.97^2 + 12.66^2 - 2(11.97)(12.66)cosACB

cos-1 = (15^2 - 11.97^2 - 12.66^2) / (-2(11.97)(12.66)) = ACB = 74.98°

 

  

CPhill  Apr 5, 2015
 #2
avatar
+5

Not sure how to give CPhill's answer a vote or thumbs up, but thank you, very helpful! 

Guest Apr 6, 2015
 #3
avatar+91435 
+5

Hi anon,

You cannot give thumbs up unless you are a member. 

If you were a member you could have give CPhill 5 points:)

Why don't you join up - there are a number of plusses to be had and absolutely no negatives :)

Melody  Apr 6, 2015

24 Online Users

avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details