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.

Guest Jun 9, 2017

#1**+2 **

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

CPhill
Jun 9, 2017

#2**0 **

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?

Guest Jun 9, 2017

edited by
Guest
Jun 9, 2017

edited by Guest Jun 9, 2017

edited by Guest Jun 9, 2017

#3**+1 **

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.....!!!

CPhill
Jun 9, 2017