Karen is looking at the edge of a large circular object from a distance. from her view, the object appears as a line segment. she knows that the distances between herself and the points on the edges of what appears to be a line segment measure 25 feet. she also knows from her location, the edges form an angle at the point she is standing at that measures 45°. find the diameter of the object that karen is looking at.

d = 25 ft

ω = (45º) ⁄ 2 = 22.5º

sin(ω) = R ⁄ d

                sin(22.5º) = R ⁄ 25

R = 9.57 feet

Diameter = 2R

Diameter = 2 • (9.57)

Diameter = 19.1 feet

Diameter = 19 feet (when rounded)

  21.3

step-by-step explanation:

multiplying the given equation by c/sin(25°), we get

  c = 9/sin(25°) ≈ 21.2958 ≈ 21.3

we assume "c" is the length of ab, the side opposite angle c in triangle abc.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is