A chord with a length of #35 # runs from #pi/8 # to #pi/2 # radians on a circle. What is the area of the circle?
1 Answer
Draw two radii to the edges of the chord to complete a triangle Then find the ratio between the angles, and apply the sine rule. Then calculate the radius and the area. (
Explanation:
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Draw two radii to the edges of the chord complete a triangle. You'll have an isosceles triangle with sides
#r# ,#r# , and 35, and angles#x# ,#x# , and#theta# . -
The edges of the chord are
#pi/8 and pi/2# , so the angle between the two radii#(theta) = pi/2 - pi/8 = {3pi}/8 "rad"# . -
The sum of all angles in a triangle
#= 180^"o" = pi " rad"#
#:. x + x+ theta = pi#
#2x + {3pi}/8 = pi#
#x = {5pi}/16# -
In any trangle
#side_1:side_2:side_3# =#sinangle_1: sinangle_2: sinangle_3#
- The area
#= pi*r^2=pi*(31.5 )^2#
#=992.2 " units"^2#