# Showing area of triangle

1. Sep 25, 2009

### zeion

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

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

Does $$\theta \epsilon (0, \pi)$$ 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: Sep 25, 2009
2. Sep 25, 2009

### Dick

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. Sep 27, 2009

### zeion

The area is bh/2

4. Sep 27, 2009

### Dick

They want you to give an answer in terms of the sides a and b. Not the base and the height.

5. Sep 27, 2009

### zeion

Can you give me a little more hint -_-;

What are the two cases that I need to consider?

6. Sep 27, 2009

### Dick

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. Sep 28, 2009

### zeion

h = b(sin theta)
or
h = b(sin 180 - theta)

8. Sep 28, 2009

### Dick

sin(theta) and sin(180-theta) are the same number. Aren't they?

9. Sep 28, 2009

### zeion

So can I show this by drawing a picture?

10. Sep 28, 2009

### Dick

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)?