The circle in the figure below has a radius of r and center at C. The distance from A to B is x. Redraw the figure below, label as indicated in the problem, and then solve the problem.
If C = 64° and x = 23, find r
Answers
Answer:cos(64°)=r/(23+r)
cos(64°)*(23+r)=r
cos(64°)*23+cos(64°)*r=r
cos(64°)*23=r-cos(64°)*r
cos(64°)*23=(1-cos(64°))*r
cos(64°)*23/(1-cos(64°))=r
14.1=r, rounds to 14.
Radius = 21.7
Step-by-step explanation:
AC = BC = r
in ΔABC
∠CAB = ∠CBA
∠C = 64°
∠CAB + ∠CBA + ∠C = 180°
=> ∠CAB = ∠CBA = 58°
Draw a line segment AB = 23
Draw angles of 58 ° at A & B on AB using protector which intersect at C
Using compass Taking width = AC or BC and C as center Draw the circle
finding r
Draw CM ⊥ AB AM = BM = 23/2
=> Cos58° = AM/AC
=> 0.53 = (23/2)/r
=> r = 21.7
Radius = 21.7
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