The diagram below shows a pentagram (a five-pointed star) inscribed inside a regular pentagon. there are several golden ratios in this figure. for example:
and .
this means that if length a = 2, then length b = 3.236. in this case, what is length c?
a.2.618
b.1.618
c.0.618
d.5.236
e.4.236

Let the angle between a and b be x then,
x = arccos((a^2 + b^2 - b^2)/2ab = arccos(a/2b)
x = arccos(2/2(3.236)) = arccos(1/3.236) = arccos(0.3090) = 80°

Thus, the angle opposite c = 180 - 80 = 100°

Therefore, c = sqrt(a^2 + b^2 - 2abcos C) = sqrt(2^2 + 3.236^2 - 2(2)(3.236)cos 100) = sqrt(14.471696 + 2.247702) = sqrt(16.719398) = 4.089
c = 4.089

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )