Question

One angle of a rhombus measures 102°, and the shorter diagonal is 4 inches long. Approximately how long is the side of the rhombus? (Hint: Diagonals of a rhombus bisect the angles.)

2 in.
3 in.
4 in.
5 in.

Answer 1

Approximately 3 inches.

Explanation:

The shorter diagonal will bisect the 102 degree angle. so we have a triangle with base angles of 51, vertex 180 - 102 = 78 degrees and base length 4 inches.

Applying the Sine Rule:

4 / sin 78 = x / sin 51 where x = the length of the side of the rhombus.

x = 4 * sin 51 / sin 78

= 3.17 inches.