Answer:
Measure of angle E is 55°
Length of the side EF is 12.49 units
Step-by-step explanation:
We are given the triangle EDF with angle measures ∠D = 43° and ∠F = 82°.
As, we know, The sum of the measures of angles in a triangle is 180°.
So, we have,
∠E + ∠D + ∠F = 180°
i.e. ∠E + 43° + 82° = 180°
i.e. ∠E = 180° - 125°
i.e. ∠E = 55°
Thus, the measure of angle E is 55°.
Further we have,
[tex]\frac{15}{\sin 55}=\frac{EF}{\sin43}[/tex]
i.e. [tex]EF=\frac{15\times \sin43}{\sin 55}[/tex]
i.e. [tex]EF=\frac{15\times 0.682}{0.819}[/tex]
i.e. [tex]EF=\frac{10.23}{0.819}[/tex]
i.e. EF = 12.49 units
Thus, the length of the side EF is 12.49 units.
