The value of DF and DG is 22.57 units and 25.9956 units respectively.
Given to us,
∠D = 48°,
∠F = 75°,
FG = 20,
According to sine rule, in a triangle the length of a side of the triangle and the angle opposite to it is always in ratio. therefore,
[tex]\dfrac{A}{sin\alpha}= \dfrac{B}{sin \beta}= \dfrac{C}{sin\gamma}[/tex]
So,
[tex]\dfrac{DF}{sin (G)}= \dfrac{FG}{sin (D)}= \dfrac{GD}{sin(F)}[/tex],
For ∠G,
∠D + ∠F + ∠G = 180°,
48° + 75° + ∠G = 180°,
∠G = 180° - ( 48° +75°),
∠G = 57°,
Now using the sine rule,
[tex]\dfrac{DF}{sin (G)}= \dfrac{FG}{sin (D)}= \dfrac{DG}{sin(F)}\\\\\\\dfrac{DF}{sin (57)}= \dfrac{20}{sin (48)}= \dfrac{DG}{sin(75)}\\\\\\\dfrac{DF}{sin (57)}= \dfrac{20}{sin (48)}\\\\DF = 22.57\ units\\\\\\ \dfrac{20}{sin (48)}= \dfrac{DG}{sin(75)}\\\\DG = 25.9956\ units[/tex]
Hence, the value of DF and DG is 22.57 units and 25.9956 units respectively.
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