Question

The length of each side of a rhombus is 10 and the measure of an angle of the rhombus is 60. Find the length of the longer diagonal of the rhombus.

Answer 1

The diagonals of a rhombus are perpendicular bisectors of each other, and are also angle bisectors. The 4 congruent right triangles the rhombus is cut into by the two diagonals are 30-60-90 degree triangles, the longer leg is √3/2 of the hypotenuse, √3/2 of 10=5√3. so the longer diagonal is twice of 5√3=10√3