The diagonals of a rhombus are 320mm and 240mm in length. Find the angles of the rhombus.provide diagrams
To find the angles of the rhombus, we first need to find the length of one side of the rhombus using the Pythagorean theorem.
Let's label the rhombus ABCD, with diagonal AC = 320mm and diagonal BD = 240mm. Let x be the length of one side of the rhombus.
Using the Pythagorean theorem, we can find x:
AC^2 = x^2 + x^2
320^2 = 2x^2
102400 = 2x^2
x^2 = 51200
x ≈ 226.27mm
Now that we have the length of one side of the rhombus, we can find the angles. Since a rhombus has all sides of equal length, we know that all angles are equal.
To find the angles, we can use trigonometry. Let's consider triangle ABC:
tan(angle) = opposite/adjacent
tan(angle) = 240/226.27
angle ≈ 47.3°
Therefore, the angles of the rhombus are approximately 47.3°.
Below is a diagram of the rhombus ABCD:
```
A
/ \
/ \
240 x
/ \
/ \
D-----------C
320
```