One diagonal of a rhombus makes a 27 degree angle with a side of the rhombus. If each side of the rhombus is 6.2 inches find the length of each diagonal to the nearest tenth.

Answer 1

Let the rhombus have vertices ABCD.
If ∡BAC = 27° then ∡BCA = 27° and ∡ABC = 126°
So, you can use law of sines or law of cosines to find AC.

Now, knowing that ∡BAD = 54° (why?), you can follow similar steps to find BD.