By applying the law of cosine, the length of side BM is equal to 7.05 cm..
What is a polygon?
A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:
Note: The number of sides (n) of a pentagon is 5.
In Geometry, the interior angle of both a regular and irregular polygon is given by this formula:
Interior angle = 180 × (n - 2)/n
Interior angle = 180 × (5 - 2)/5
Interior angle = 180 × 3/2
Interior angle = 108°.
For the central angle, we have:
Central angle, O = 360/5
Central angle, O = 72°.
By applying the theorem of intersecting secants, angle OCB will be given by this formula:
<OCB = ½ × (180 - 72)
<OCB = ½ × 108
<OCB = 54°.
In order to determine the length of side BM, we would apply the law of cosine:
cos(θ) = Adj/Hyp
cos54 = BM/12
BM = 12 × cos54
BM = 12 × 0.5878
Side BM = 7.05 cm.
Read more on law of cosine here: brainly.com/question/27613782
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