Perpendicular Bisector of a triangle

  • #1
nmnna
22
3
Homework Statement:
##ABC## is a triangle such that ##\angle ABC = 37^{\circ}15'##, ##\angle ACB = 59^{\circ}40'##, ##BC = 8## cm; the perpendicular bisector of ##BC## cuts ##BA##, ##CA## produced at ##P, \ Q##. Find the length of ##PQ##.
Relevant Equations:
##\tan(\alpha) = \frac{opposite \ side}{adjacent \ side}##
Here is my attempt to draw a diagram for this problem:
1617268604102.png

I'm confused about the "the perpendicular bisector of ##BC## cuts ##BA##, ##CA## produced at ##P, \ Q##" part of the problem.
How does perpendicular bisector of ##BC## cut the side ##CA##?
 

Answers and Replies

  • #2
mjc123
Science Advisor
Homework Helper
1,271
679
It cuts CA produced. Extend the line CA until it meets the bisector. That point is Q (not where you have put it).
 
  • Like
Likes nmnna and FactChecker
  • #3
nmnna
22
3
It cuts CA produced. Extend the line CA until it meets the bisector. That point is Q (not where you have put it).
Thank you
 
  • #4
nmnna
22
3
It cuts CA produced. Extend the line CA until it meets the bisector. That point is Q (not where you have put it).
1617290558617.png

I changed my diagram.
Now I have the right triangle ##\triangle PQC##, where ##CP = 4##cm (since ##PQ## is a perpendicular bisector), ##\angle QCP = 59^{\circ}40'##, so I can find ##PQ## using the relation $$\tan\angle QCP = \frac{PQ}{CP}$$
I got ##\approx 6.818## which is not the answer given in my textbook. Where did I go wrong?
 
Last edited:
  • #5
Lnewqban
Gold Member
2,434
1,290
View attachment 280723
I changed my diagram.
Now I have the right triangle ##\triangle PQC##, where ##CP = 4##cm (since ##PQ## is a perpendicular bisector), ##\angle QCP = 59^{\circ}40'##, so I can find ##PQ## using the relation $$\tan\angle QCP = \frac{PQ}{CP}$$
I got ##\approx 6.818## which is not the answer given in my textbook. Where did I go wrong?
The description seems confusing to me as well.
Could it be that point P should be located where the perpendicular bisector of BC cuts BA?
What is the answer given in your textbook?
If it is close to 3.75 cm, then your last diagram is not correct regarding location of P.
 
  • #6
mjc123
Science Advisor
Homework Helper
1,271
679
P is the point you have called L. The original statement, which is perhaps not as clear as it might be, means "the perpendicular bisector of BC cuts BA at P and cuts CA produced at Q."
 
  • Like
Likes nmnna and Lnewqban
  • #7
nmnna
22
3
P is the point you have called L. The original statement, which is perhaps not as clear as it might be, means "the perpendicular bisector of BC cuts BA at P and cuts CA produced at Q."
Thank you for your help.
 

Suggested for: Perpendicular Bisector of a triangle

Replies
9
Views
317
  • Last Post
Replies
4
Views
671
  • Last Post
Replies
11
Views
293
Replies
3
Views
270
  • Last Post
Replies
5
Views
229
Replies
7
Views
965
Replies
40
Views
1K
Replies
27
Views
349
Replies
4
Views
594
Replies
2
Views
443
Top