Step 1: Find the side lengths of the rhombus.
Let represent the point of intersection of the diagonals.
The diagonals of a rhombus form angles. So, .
The diagonals of a rhombus also bisect each other. Therefore,
To find the length of , use Pythagoras' theorem. Substitute the known lengths in ,
and solve for the length of . (Approximate to the nearest hundredth.)
All sides of a rhombus are of equal length. Therefore,
Step 2: Classify .
If the square length of a triangle's longest side is less than the sum of the square lengths of the other two sides, then the triangle is acute.
(Approximate to the nearest hundredth.)
Hence, is an acute triangle.