Answer:
DF = 10 units
[tex]m\angle DFG = 28^\circ[/tex]
EG = 5.04
Step-by-step explanation:
Properties of Rhombus
es
- All Sides Of The Rhombus Are Equal.
- The Opposite Sides Of A Rhombus Are Parallel.
- Opposite Angles Of A Rhombus Are Equal.
- In A Rhombus, Diagonals Bisect Each Other At Right Angles.
- Diagonals Bisect The Angles Of A Rhombus.
The image contains a rhombus with the following data (assume the center as point O):
DO = 5 units
GF = 5.6 units
[tex]m\angle FEO = 62^\circ[/tex]
4. Calculate DF
Applying property 4, diagonals bisect each other, thus the length of DF is double the length of DO, i.e. DF=2*5 = 10:
DF = 10 units
5. Calculate [tex]m\angle DFG[/tex]
Applying property 4 in triangle EFO, the center angle is 90°, thus angle EFO has a measure of 90°-62°=28°.
Applying property 5, this angle is half of the measure of angle EFG and angle DFG has the same measure of 28°.
[tex]m\angle DFG = 28^\circ[/tex]
6. FG is the hypotenuse of triangle OFG, thus:
[tex]OG^2=FG^2-OF^2[/tex]
[tex]OG^2=5.6^2-5^2[/tex]
[tex]OG^2=6.36[/tex]
[tex]OG=\sqrt{6.36}=2.52[/tex]
EG is double OG: OG=2*2.52=5.04
EG = 5.04
