Question

A rhombus has diagonals of 32 and 20 inches. Find the angle of opposite the longer diagonal

Answer 1

Rhombus side

$a=\sqrt{16^2+10^2}=\sqrt{356},$

$angle=2\arcsin{\frac{16}{a}}=2\arcsin{\frac{16}{\sqrt{356}}}\approx 116^{\circ}.$

Answer: the angle is approximately equal to 116 degrees.