Question

the lengths of the diagonal of a rhombus are 2 in and 5 in.
find the measure of the angles of the rhombus to the nearest degree.

if it helps, we are learning how to use tangent right now!

Answer 1

Draw a rhombus with the diagonals.

4 right triangles are formed.

The intersection of the diagonals of a rhombus form 90 degree (right) angles (property of a rhombus).

The diagonals of a rhombus bisect each other. This means that they cut each other in half.

So, each of the right triangles have one side = 1, one side = 2.5 and the hypotenuse = unknown (sides of the
rhombus).

Triangle 1. ABC
side a = 2.5, side b = 1
tan A = a/b = 2.5/1 = 2.5
tan A = 2.5
tan 68.2 deg = 2.5

Since, angle C = 90 and angle A = 68.2
angle B = 21.8 deg. (180 - (90 + 68.2))

Since, the diagonals bisect angles in each corner of a rhombus (property of a rhombus), therefore, one corner angle is 68.2 + 68.2 = 136.4 deg. and the same side other corner angle is 21.8 + 21.8 = 43.6 deg.

Adjacent sides (ones next to each other) of a rhombus are supplementary. This means that their measures add up to 180 degrees.

Therefore, the opposite corners are
180 - 136.4 = 43.6 and
180 - 43.6 = 136.4.

So, the four angles are,
136.4, 43.6, 136.4, and 43.6