Question

how to calculate the acute angle between the diagonal of the rectangle

Answer 1

acute angle between diagonals of a rectangle will always be 90°

Answer 2

Name the rectangle ABCD,letting the larger side be AB(7cm) and the smaller side be AC(5cm). Draw the two diagonals across the rectangle. Name the point of intersection of the two diagonals (which resembles an X) F. Name the midpoint between the smaller side AC, to be E.
AFC is the acute angle you are looking for, angle AFE is half of that.
So AFE is a right angled triangle and AE is equal to half of 5cm, which is 2.5; FE is equal to half of 7cm, which is 3.5.
Now, taking triangle AFE,
Tan AFE=2.5/3.5
AFE=35.537 degrees
Since the angle AFE is half of the acute angle AFC that you are looking for,
multiply AFE into two
So, 35.537*2
=71.075 degrees
=71.1 degrees (to 1 decimal place)
AFC= 71.1 (ANS). thnk u..