A circle has a chord that goes from #( pi)/8 # to #(4 pi) / 3 # radians on the circle. If the area of the circle is #75 pi #, what is the length of the chord?
1 Answer
Sep 7, 2017
Explanation:
#"calculate the length of the chord using the "color(blue)"cosine rule"#
#color(red)(bar(ul(|color(white)(2/2)color(black)(c^2=a^2+b^2-(2abcosC)color(white)(2/2)|)))#
#"where c is the length of the chord, a and b are the radii"#
#"and C is the angle subtended at the centre of the circle"#
#"by the chord"#
#pir^2=75pilarr" area of circle"#
#rArrr^2=75rArrr=+-sqrt75=5sqrt3#
#angleC=(4pi)/3-pi/8=(32pi)/24-(3pi)/24=(29pi)/24#
#c^2=(5sqrt3)^2+(5sqrt3)^2-(2xx5sqrt3xx5sqrt3xxcos((29pi)/24))#
#color(white)(c^2)=75+75-(-119)=269#
#rArrc=sqrt269~~ 16.4" units"#
