Answer:
True Statement are
[tex]\sin E =\dfrac{11}{\sqrt{185}}[/tex]
[tex]\sin D =\dfrac{8}{\sqrt{185}}[/tex]
Step-by-step explanation:
Given:
DF = 11
EF = 8
[tex]DE = \sqrt{185}=Hypotenuse[/tex]
In Right Angle Triangle DEF, the Sine Identity is
[tex]\sin D = \dfrac{\textrm{side opposite to angle D}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\sin D = \dfrac{EF}{DE}=\dfrac{8}{\sqrt{185}}[/tex]
[tex]\sin D =\dfrac{8}{\sqrt{185}}[/tex] ....True
And also,
[tex]\sin E = \dfrac{\textrm{side opposite to angle E}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\sin E = \dfrac{DF}{DE}=\dfrac{11}{\sqrt{185}}[/tex]
[tex]\sin E =\dfrac{11}{\sqrt{185}}[/tex] ....True
