A rhombus has diagonals of lengths 6 cm and 9 cm. Calculate the sizes of it's interior vertex angles.

Question

The diagonals of a rhombus bisect each other and cross at right angles.

Answer 1

Diagonals are mutually bisecting.

 

The large interior angle is 2 tan^-1 1.5.   (4.5 / 3)

Consecutive angles are complementary.

Answer 2

Both Norbert and Mark got the same answer, but they solved for a different interior angle so their

equations using tan^-1 are different. 

 

To me, it seems unnecessary for Norbert to solve for the side of the rhombus:

"Then the side of the rhombus is √(6/2)2 + (9/2)2) = √(9 + 81/4) = 3√(13)/2"

 

 

Answer 3

Since the rhombus is a parallelogram, its diagonals bisect each.

Also, the diagonals are perpendicular.

 

Then the side of the rhombus is √(6/2)² + (9/2)²) = √(9 + 81/4) = 3√(13)/2

 

Let θ be one of the interior angles.  Then θ = 2 * tan-1(3/4.5) = 2 * tan-1(2/3) ≈ 67.38° and the other angle is 180 - 2 * tan-1(2/3) ≈ 112.62 °