Question

Find the acute angle between the sides of a rhombus whose diagonals are 8cm and 12cm long

Answer 1

67.38°

Explanation:

The diagonals of a rhombus intersect at their midpoints and make a right angle. They also divide the angles of the rhombus in two equal angles.

So, to find the acute angle of the rhombus, we can use the tangent relation of half this angle in the small triangle made when drawing the diagonals:

tan(angle/2) = 4 / 6

tan(angle/2) = 0.666

angle/2 = 33.69

angle = 67.38°

So the acute angle of the rhombus is 67.38 degrees.

Please check the image attached for better comprehension.