Final answer:
By calculating the cosine of the angle, we find that the angles of the rhombus are approximately 19.15°.
Step-by-step explanation:
A rhombus is a quadrilateral with all sides of equal length.
In order to find the angles of a rhombus, we need to use the lengths of the diagonals. Let's label the diagonals as D1 and D2.
The length of D1 is 4.73 and the length of D2 is 2.94.
Since the diagonals of a rhombus bisect each other at right angles, we can use the formula:
D1^2 = (d1/2)^2 + (d2/2)^2
Substituting the given values:
D1^2 = (4.73/2)^2 + (2.94/2)^2
D1^2 = 2.365^2 + 1.47^2
D1^2 = 5.572225 + 2.1609
D1^2 = 7.733025
D1 = √7.733025
D1 ≈ 2.781
Now, let's find the measure of the angle:
cos(θ) = (D1/2.94)
cos(θ) = (2.781/2.94)
θ ≈ arccos(0.945)
θ ≈ 19.15°
Therefore, the angles of the rhombus are approximately 19.15°.