Question

Where does the formula with respect to any triangle
\(Area=\frac{1}{2} absin\theta\) come from?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

add in a perpendicular to line 'a', call it h

Answer 5

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

Answer 6

we can use trig to say

sin(theta) = h/b
h = b*sin(theta)

Answer 7

then do a substitution

Answer 8

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

Answer 9

you're welcome

Answer 10

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

Answer 11

oh, cause you use 180-theta

Answer 12

extend out segment a until it's a line



make sure that the tip is over the line

Answer 13

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

Answer 14

(test tomorrow, Praxis)

Answer 15

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

Answer 16

good luck on it tomorrow

Answer 17

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

Answer 18

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)

Answer 19

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!