Question

Given DFG, mD=48° mF=75°, FG= 20 Find DF,DG

Answer 1

Answer:

DF=22.57

DG=26

Step-by-step explanation:

sinF/DG=sinD/FG

sin75/DG=sin48/20

DG*sin48/sin48=20*sin75/sin48

DG=26

D^+F^+G=180(sum of int. angles of triangle)

G^=180-48-75

G^=57

sinG/DF=sinD/FG

sin57/DF=sin48/20

DF*sin48/sin48=20*sin57/sin48

DF=22.57

Answer 2

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,

$\dfrac{A}{sin\alpha}= \dfrac{B}{sin \beta}= \dfrac{C}{sin\gamma}$

So,

$\dfrac{DF}{sin (G)}= \dfrac{FG}{sin (D)}= \dfrac{GD}{sin(F)}$,

For ∠G,

∠D + ∠F + ∠G = 180°,

48° + 75° + ∠G = 180°,

∠G = 180° - ( 48° +75°),

∠G = 57°,

Now using the sine rule,

$\dfrac{DF}{sin (G)}= \dfrac{FG}{sin (D)}= \dfrac{DG}{sin(F)}\\\\\\\dfrac{DF}{sin (57)}= \dfrac{20}{sin (48)}= \dfrac{DG}{sin(75)}\\\\\\\dfrac{DF}{sin (57)}= \dfrac{20}{sin (48)}\\\\DF = 22.57\ units\\\\\\ \dfrac{20}{sin (48)}= \dfrac{DG}{sin(75)}\\\\DG = 25.9956\ units$

Hence, the value of DF and DG is 22.57 units and 25.9956 units respectively.

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