Question

A rhombus has sides of length 150 centimeters, and the angle at one of the vertices is 50°. Approximate the lengths of the diagonals to the nearest tenth of a centimeter.

Answer 1

In a rhombus, the diagonals bisect each other, so in my diagram, BE = ED.

Also, in a rhombus, a diagonal bisects a vertex of the rhombus. So angle EAB = 25 degrees.

Also, the diagonals are perpendicular to each other, so they form right angles.

Answer 2

So we will find x, the length of BE using a trig equation:

sin (25) = x/150

Cross-multiply, you get x = 150 (sin 25)
x = 63.39274

So BE = ED = 63.39274, therefore, the entire diagonal
BD = 2(63.39274)
= 126.786

Answer 3

So we found thelength of one entire diagonal. Now, you do the same for the other diagonal, AC.