A regular 9 sided building is 814 ft along one side what is the distance from a Vertex to the center of the building
we know that
A regular 9 sided polygon, can be divided into 9 isosceles triangle
The equal distances of the isosceles triangle is equal to the radius or the distance from a Vertex to the center of the building
the base of the isosceles triangle is given and is equal to 814 ft
The measure of the interior angle of the vertex is equal to
360/9=40 degrees
that means
we have
Applying the law of sines
814/sin(40)=r/sin(70)
solve for r
r=(814/sin(40))*sin(70)
r=1,190 ft
therefore
the distance is 1,190 ft