Currently stuck at this question; calculate what a and b stand for, also calculate the area of the triangle.
The problem is that I have no idea what to to get the x into a grade value.
+130555
Since the apex angle = 2x, the side opposite it will have the same measure as the side opposite the other angle measuring 2x = 27 cm
So
a + b = 27 (1)
And since the apex angle is bisected we have that
a/b = 11/27
27 a = 11b
a = (11/27)b (2)
Subbing (2) into (1) we have that
(11/27)b + b = 27
(38/27)b = 27 multipyl both sides by (27/38)
b = 27^2/38 = 729/38 cm
And a = (11/27)b = (11/27) (729/38) = 27 * 11 / 38 = 297/38 cm
We can use something called Heron's Formula to find the area
Area = sqrt [ s (s -a) (s - b) (s - c) ]
Where a, b, c are the sides and s is the semi-perimeter = [ a + b + c] / 2 =
[ 11 + 27 + 27 ] / 2 = 65/2 = 32.5 cm
So...the area is
sqrt [ 32.5 (32.5 - 11) (32.5 - 27) (32.5 - 27) ] = 145.39 cm^2
Notice that we didn't actually have to find out what "x" was, at all...but....you could certainly do that using the Law of Cosines
Thank you for the explanation!
Since the apex angle = 2x, the side opposite it will have the same measure as the side opposite the other angle measuring 2x = 27 cm
Why is it like that though?
+130555
Thanks.....!!!
Look at Euclid's proof related to your question :
http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI6.html
It's not too hard to understand.....!!!
