The length of each side of a rhombus is 16. The longer diagonal has length 26. Find the measures of the angles of the rhombus to the nearest degree.

Question

anonymous · Answer

@phi

phi · Answer

First, refresh your memory on the properties of a rhombus http://www.mathsisfun.com/geometry/rhombus.html

phi · Answer

The key property is the last one they mention.

phi · Answer

First step, can you draw a picture for this problem ?

anonymous · Answer

|dw:1367168641009:dw|

phi · Answer

yes,  but add the other diagonal
|dw:1367168826643:dw|

if you made all 4 sides the same length (as they really are) the picture would look better.
The key fact is that the diagonals form a right angle,   and bisect each other.
that means we have 4 identical right triangles.