SOLUTION: how do I find the area of an iscoseles triangle when I've only been given the measurements of two sides using the sine rule: 1/2(ab)sinC

Algebra ->  Triangles -> SOLUTION: how do I find the area of an iscoseles triangle when I've only been given the measurements of two sides using the sine rule: 1/2(ab)sinC       Log On


   

Question 674343: how do I find the area of an iscoseles triangle when I've only been given the measurements of two sides using the sine rule: 1/2(ab)sinC
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the formula you are using is area of a triangle is equal to 1/2 * base * height.
the base is a
the height is b * sin(c)
my diagram of your triangle is shown below:
$$$$$$$
in the diagram, h is the height and a is the base.
using trigonometry, we get:
sin(c) = oppositve / hypotenuse = h / b
multiplying both sides of this equation by b, we get:
h = b * sin(c)
since they're equal, we can substitute one for the other.
the formula is area = 1/2 * base * height.
the base is equal to a.
the height is equal to b * sin(c)
the formula becomes:
area = 1/2 * a * b * sin(c)
to find the area of the triangle using this formula, you need to know what angle C is.