Answer:
A. 13.31' to the nearest hundredth.
B. 86.52' to the nearest hundredth.
Step-by-step explanation:
Part A>
The apotherm of a regular polygon is the distance of the line segment from the centre of the polygon to the midpoint of a side.
2 radii of this decagon joined to the endpoints of a side form an isosceles triangle with equal sides = 14 cm.
The apotherm is the altitude of this triangle. The vertex of the triangle has an angle of 360 / 10 = 36 degrees and the apotherm bisects this angle.
So using trigonometry on the right triangle formed:
cos 18 = x / 14 where x is the apotherm.
x = 14 cos 18
= 13.31' (answer).
Part B.
Using trigonometry on the right triangle again:
sin 18 = x/2 / 14 (where x is the length of a side of the hexagon)
x/2 = 14 sin 18
x = 2 * 14 sin 18
= 8.652'.
As a decagon has 10 sides the perimeter = 8.652 * 10
= 86.52' to the nearest hundredth.
