Mathematics - Properties of Triangle Question with Solution | TestHub

B=C=80°, b=c. Sine rule gives a/b=sin20°/sin80°=2sin10°. The triple-angle identity sin30°=3sin10°-$4si{n}^3$10° implies $8si{n}^3$10°+1=6sin10°. Therefore $a^3$+$b^3$=$b^3$($8si{n}^3$10°+1)=$6b^3$sin10°=$3a{b}^2$=$3a{c}^2$.