SOLUTION: a road 12 m wide runs through a tunnel 18m high the cross section of the tunnel is a major segment of a circle calcute the radius of the circle

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Question 365014: a road 12 m wide runs through a tunnel 18m high the cross section of the tunnel is a major segment of a circle calcute the radius of the circle
Answer by CharlesG2(834) About Me  (Show Source):
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a road 12 m wide runs through a tunnel 18m high the cross section of the tunnel is a major segment of a circle calcute the radius of the circle

major segment of a circle is the region of a circle bounded by the chord and the major arc intercepted by the chord

road 12 m wide = the chord
tunnel 18 m high = height of the major segment
1/2 chord = 6 meters
right triangle with opposite side = 6 meters
and adjacent side = height = 18 meters
use Pythagorean Theorem to get hypotenuse
6^2 + 18^2 = hyp^2
36 + 324 = 360 = hyp^2
36 * 10 = hyp^2
6sqrt(10) = hypotenuse = 18.973666 rounded to 6 places
sin = opp/hyp = 6/(6sqrt(10)) = 1/sqrt(10) = 0.316228 to 6 places
this is an angle of 18.434949 degrees rounded to 6 places
whole angle (the central angle) is twice the above angle and is 36.869898 degrees rounded to 6 places
half chord length = 6
sin 18.434949 = 6/radius
radius * sin 18.434949 = 6
radius = 6/(sin 18.434949)
radius = 18.973666 rounded to 6 places = 6sqrt(10)