## FibonacciChick666 one year ago Where does the formula with respect to any triangle $$Area=\frac{1}{2} absin\theta$$ come from?

1. ganeshie8

Area of triangle with sides $$\vec{a},~~\vec{b}$$ is given by $$\dfrac{1}{2}\vec{a}\times \vec{b}$$

2. FibonacciChick666

I know, but this book is claiming that for any type of triangle the area formula stated above.

3. jim_thompson5910

|dw:1444016348537:dw|

4. FibonacciChick666

yea that's the rep. if you want the specific Q I can give that to you

5. jim_thompson5910

add in a perpendicular to line 'a', call it h |dw:1444016388804:dw|

6. jim_thompson5910

if we know h, we can compute the area to be a*h/2

7. jim_thompson5910

we can use trig to say sin(theta) = h/b h = b*sin(theta)

8. jim_thompson5910

then do a substitution

9. FibonacciChick666

thank you. It just wasn't happening for me there

10. jim_thompson5910

you're welcome

11. FibonacciChick666

sorry, I more thing. If the angle is obtuse, why does this work?

12. jim_thompson5910

|dw:1444016751760:dw|

13. FibonacciChick666

oh, cause you use 180-theta

14. jim_thompson5910

extend out segment a until it's a line |dw:1444016801093:dw| make sure that the tip is over the line

15. FibonacciChick666

thank you! I'm sorry this test is making me lose my mind

16. FibonacciChick666

(test tomorrow, Praxis)

17. jim_thompson5910

|dw:1444016826079:dw|

18. jim_thompson5910

and i'm sure at this point you can see how sin(180 - theta) = h/b and you can do a bit of manipulation to end up with the same formula

19. jim_thompson5910

good luck on it tomorrow

20. FibonacciChick666

Thanks... I'm just worried. It's been years since most of this stuff

21. jim_thompson5910

http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf idk where on the sheet (if it's even on there), but one identity is sin(pi - x) = sin(x) sin(180 - x) = sin(x)

22. FibonacciChick666

Thanks! Yea, this is the math specific praxis. I'm good on most stuff, but I get really really really bad test anxiety so any extra study material is appreciated!