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# Natasha Octagon

+6
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5 Jun 25, 2014

#5
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Let's do "b" first.....since this is an octagon. the measure of <AOB = 360/8 = 45

And m<AOX is 1/2 of that = 22.5

And that's a  and b

c) Note that the measure of <OAX = 90- 22.5 = 67.5

And we can find OX by the Law of Sines

OX/sin67.5 = OA/sin90 ......  (sin 90 = 1)

OX/sin67.5 = 9

OX = 9sin67.5 = about 8.3m

d) We can find AB with the Law of Cosines

AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos45

AB^2 = 9^2 + 9^2 - 2(9)(9)cos45

AB^2 = 162 - 162cos45 = 47.448701447706    take the square root of both sides

AB =  about 6.9m

e) The perimeter = 8(6.9)= about 55.2 m

f) Area...we have 8 congruent triangles....the area of each is given by (1/2)(9^2)sin45 = 28.6378246380735m^2

So.... 8*28.6378246380735 = about 229m^2

Hope I haven't made any serious errors here.....!!!   Jun 25, 2014

#1
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Can i ask u CPhill whos Natasha!becoz ive just heard one name like this"Natasza"! so whos "Natasha "now! Jun 25, 2014
#2
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I am Polish, So It Is Spellt Natasza! :) But American Spell it Natasha. Poor CPhill had Typoes with it! lol My Email Was Spellt Natasha so...Thats Why He Spell It Like That

Jun 25, 2014
#3
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oh thats why hes spelling it like that!but btw i have no problem spelling it i can simply say "Natasza" thats easy!and natasza r these questions by u!? i never saw u posting them! Jun 25, 2014
#4
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Haha thats Okay! :) It is Pronounced Sort of The Same! These Questions Are Not Mine.

Jun 25, 2014
#5
+8

Let's do "b" first.....since this is an octagon. the measure of <AOB = 360/8 = 45

And m<AOX is 1/2 of that = 22.5

And that's a  and b

c) Note that the measure of <OAX = 90- 22.5 = 67.5

And we can find OX by the Law of Sines

OX/sin67.5 = OA/sin90 ......  (sin 90 = 1)

OX/sin67.5 = 9

OX = 9sin67.5 = about 8.3m

d) We can find AB with the Law of Cosines

AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos45

AB^2 = 9^2 + 9^2 - 2(9)(9)cos45

AB^2 = 162 - 162cos45 = 47.448701447706    take the square root of both sides

AB =  about 6.9m

e) The perimeter = 8(6.9)= about 55.2 m

f) Area...we have 8 congruent triangles....the area of each is given by (1/2)(9^2)sin45 = 28.6378246380735m^2

So.... 8*28.6378246380735 = about 229m^2

Hope I haven't made any serious errors here.....!!!   CPhill Jun 25, 2014