1. ## Hexagon Angles/Trig.

Hey guys, I have this assignment due on Monday and I have done all of it except for the last question. I am in Year 10 level 1 Maths.

Here is the questions.

Mr X is constructing a hexagonal pergola in his backyard. The roof of the pergola needs to be 7 metres wide (from one side to its opposite, not vertex to vertex). The top view of the pergola is a regular hexagon and is shown in the diagram below.

A) Calculate the interior angle of each vertex of the pergola.
Notes: Ok I think this has to do with the sin/cosine rule, but I just don't know the equations for this.

B) Using the cosine rule and not the tangent ratio, calculate how long each side must be to achieve an overall width of 7 metres as stated above.

C) If Mr X placed guttering around the perimeter of the roof, what is the minimum length of guttering required?
Notes: No idea aswell :|

Yeah so I pretty much need help with these, if someone can try and do it, I thank you.

2. A) no cosine/sine rule here..

use this:
[(n-2) * 180]/n = angle of 1 vertex = x
n = number of vertices (6)

B) draw lines from each vertex to the center of hexagon so you'll see the triangles.
all sides of a chosen triangle are the same length = a

((a^2 = a^2 + a^2 - 2 * a * a * cos (x/2)
x = the angle you calculated in A) section. << just to show the cosine rule.. you get nothing from that without knowing a))

better way is to use this.. 2 * [(a * sqrt (3))/2] = 7
you can compare the results.. should be the same.

C) what's a guttering? xD
hmm.. 6a?

3. C is pretty much asking to find the smallest perimeter possible with your answers to B. I think.

4. C) is 6a then.

and I remembered another way for B)
c = 7
c^2 = a^2 * a^2 - (2 * a * a * cos (x))

5. attachment..