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 Simple trigo (Posted on 2014-01-03)
Find the value of

(i)cos 36
(ii)tan 15

using geometry.

 No Solution Yet Submitted by Danish Ahmed Khan No Rating

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 No Subject | Comment 2 of 6 |

Draw a 36o-72o-72o triangle, with two long sides = 1, and the short side = x .

Now, bisect one of the 72° angles forming two triangles:
a 36o-36o-108o isosceles triangle whose short sides are both x , and a smaller 36o-72o-72o isosceles triangle whose long
sides are x , and short side is 1−x

Since the two 36o-72o-72o triangles are proportional: <o:p></o:p>

x/1=(1-x)/x

solving      x2+x-1=0

we get   x=(-1+sqrt(5))/2

a.k.a.     phi, the golden ratio<o:p></o:p>

Now bisect the obtuse angle in the 36o-36o-108o triangle to    get a right
(36o-54o-90o) triangle, with a hypotenuse=(-1+sqrt(5))/2  and the long leg =1/2 .

so:

cos 36° =1/(-1+sqrt(5))=(1+phi)/2  =.809 approximately.

 Posted by Ady TZIDON on 2014-01-03 15:46:14

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