SOLUTION: Hi, I know that the area of a triangle is 1/2 bh but that is not one of the answers. How can I find the area in this triangle? Thanks. <a href="http://s571.photobucket.com/

Algebra ->  Surface-area -> SOLUTION: Hi, I know that the area of a triangle is 1/2 bh but that is not one of the answers. How can I find the area in this triangle? Thanks. <a href="http://s571.photobucket.com/      Log On


   

Question 823989: Hi,
I know that the area of a triangle is 1/2 bh but that is not one of the answers.
How can I find the area in this triangle?
Thanks.
photo 2013-12-21-c.jpg
Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h = a*sin(t)

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Rule:

Area of Triangle = (Base)*(Height)/2

Note: the base and height are ALWAYS perpendicular segments

Since h is the height (given and fixed), this forces us to choose b as the base since b is perpendicular to h

So....

Area of Triangle = (Base)*(Height)/2

A = b*h/2

-------------------------------------------------------

Now focus on the smaller triangle on the left (with hypotenuse 'a' and leg 'h')

sin(angle) = opposite/hypotenuse

sin(theta) = h/a

a*sin(theta) = h

h = a*sin(theta)

-------------------------------------------------------

Now go back to the area of a triangle equation and plug h = a*sin(theta) in

A = b*h/2

A = (1/2)*b*h

A = (1/2)*b*(a*sin(theta))

A = (1/2)ab*sin(theta)

So the answer is choice D