Showing area of triangle

  • Thread starter zeion
  • Start date
  • #1
467
0

Homework Statement



Show that for all [tex]\theta \epsilon (0, \pi)[/tex], the area of a triangle with side lengths a and b with included angle [tex]\theta is A = \frac{1}{2} a b sin \theta[/tex]. (Hint: You need to consider two cases)

Homework Equations





The Attempt at a Solution



I have just begun working on this problem.. not really sure where to start.

Does [tex]\theta \epsilon (0, \pi)[/tex] mean that the angle is > than 0 and < than pi?
Am I supposed to show that when the angle is less than or greater than the condition then the equation to find area is not valid?
 
Last edited:

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,263
619
Yes, that's what (0,pi) means. The only cases where the area is not ab*sin(theta) is where sin(theta) might be negative. They aren't in (0,pi). What's the area in that case?
 
  • #3
467
0
The area is bh/2
 
  • #4
Dick
Science Advisor
Homework Helper
26,263
619
The area is bh/2

They want you to give an answer in terms of the sides a and b. Not the base and the height.
 
  • #5
467
0
Can you give me a little more hint -_-;

What are the two cases that I need to consider?
 
  • #6
Dick
Science Advisor
Homework Helper
26,263
619
Can you give me a little more hint -_-;

What are the two cases that I need to consider?

Use trig and A=bh/2. What's h in terms of a and the included angle? Draw a right triangle. And I'm really not sure what the 'two cases' they are talking about are.
 
  • #7
467
0
h = b(sin theta)
or
h = b(sin 180 - theta)
 
  • #8
Dick
Science Advisor
Homework Helper
26,263
619
sin(theta) and sin(180-theta) are the same number. Aren't they?
 
  • #9
467
0
So can I show this by drawing a picture?
 
  • #10
Dick
Science Advisor
Homework Helper
26,263
619
There's a variety of ways to draw a picture to show sin(pi-x)=sin(x). Which sort did you have in mind? How do you picture sin(x)?
 

Related Threads on Showing area of triangle

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
5K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
2
Views
8K
  • Last Post
Replies
2
Views
25K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
4K
  • Poll
  • Last Post
Replies
5
Views
8K
  • Last Post
Replies
5
Views
940
Top