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# Triangle values

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300
5

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
+90023
+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
edited by CPhill  Jun 9, 2017
edited by 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
#3
+90023
+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
#4
0

OH RIGHT!

God I'm so dumb, totally forgot that rule existed!

Thank you for everything!

Guest Jun 9, 2017
#5
0

Weoeoeoeo

Guest Jun 9, 2017
edited by Guest  Jun 9, 2017