Question

GEOMETRY QUESTION: if the radius of your circular pattern is 6 inches, calculate the perimeter of the triangle inscribed in the circle

Answer 1

stop drawing my diagrams. ;-;

Answer 2

you ninja.

Answer 3

LOL sowwies.

Answer 4

@lncognlto so each radius is 6....

Answer 5

Yup, that is correct.

Answer 6

@lncognlto how do i go about calculating the perimeter of the triangle from that point on?

Answer 7

I would use the Law of Sines to determine the hypotenus

Answer 8

As this is an equilateral triangle, each of the inner angles is going to be 120 degrees. So then I would use the cosine rule to determine the length of one side of the triangle, and then multiply by three.

Answer 9

Well, the sin rule should work too, if you want.

Answer 10

*sine

Answer 11

so if thats the diagram then you set up SOHCAHTOA to work it out right @lncognlto

Answer 12

Yep, that should sort it. ^-^

Answer 13

You don't really need to break it down that much; you could take (sin 120)/x = (sin 30)/6 and solve for the side length from there.

Answer 14

I got 10.392 as my final answer; does that sound right? @lncognlto

Answer 15

Well, that is certainly the length of one side of the triangle, yes, but it is not the entire perimeter of it...

Answer 16

So the whole perimeter is 31.176? @lncognlto

Answer 17

Actually I don't think thats exactly right method.

Answer 18

@vishweshshrimali5 what would be the right method?

Answer 19

I would prefer using the formula for circumradius

Answer 20

I think that may work

Answer 21

Yes, I am curious... but that was the answer I got too, @ontour

Answer 22

@lncognlto i mean that got me what sounds like a reasonable answer

Answer 23

@lncognlto also, how would i calculate the area of the triangle if it had the same radius measurements

Answer 24

could someone please tell me how to calculate the area??

Answer 25

Sorry, I'm having a look... I'd do it like this, although this is not the only way:

Answer 26

I'd solve for x by Pythag, and then I would use the formula A = (1/2)bh for a triangle to get the area.

Answer 27

My final answer worked out to be 23.3723 @lncognlto

Answer 28

I get double that as my answer: 46.74...

Answer 29

How did you get it doubled? @lncognlto

Answer 30

10.39^2 - 5.195^2 = x^2
Therefore x = sqrt(10.39^2 - 5.195^2)
= 8.998
Therefore A = (0.5)bh
= (0.5)(10.39)(8.998)
= 46.74....

Answer 31

pythagorean theorem is a2+b2=c2 right?? @lncognlto

Answer 32

Yes; in this case, pythag would be 5.195^2 + x^2 = 10.39^2. So then we solve for x.

Answer 33

@ontour is this triangle equilateral or any general triangle ?

Answer 34

It's equilateral...

Answer 35

Ohh

Answer 36

You could also have used solutions of triangle's formula and would have found out area and perimeter using trigonometry. But @incognIto 's mthod is also correct. I didn't know that it was equilateral.

Answer 37

I know there is a way to calculate the area by use of trig, but I'd have to look it up again. But yeah, that would be an equally valid method.