Respuesta :

gmany

Answer:

61.19 inches

Step-by-step explanation:

Use the sine law:

[tex]\dfrac{DE}{\sin(\angle F)}=\dfrac{EF}{\sin(\angle D)}[/tex]

We have:

[tex]DE=75\ in\\\\m\angle F=75^o\to\sin75^o\approx0.9659\\\\m\angle D=52^o\to\sin52^o\approx0.788[/tex]

Substitute:

[tex]\dfrac{75}{0.9659}=\dfrac{EF}{0.788}[/tex]          cross multiply

[tex]0.9659EF=(75)(0.788)[/tex]

[tex]0.9659EF=59.1[/tex]          divide both sides by 0.9659

[tex]EF\approx61.19[/tex]

The length of the EF is 61.19 inches if the  DE = 75 inches option fourth is correct.

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have:

DE = 75 inches

By using the sin law:

sin52/EF = sin75/DE

sin52/EF = sin75/75

sin52/EF = 0.0128

EF = 61.185 ≈ 61.19 inches

Thus, the length of the EF is 61.19 inches if the  DE = 75 inches option fourth is correct.

Learn more about the triangle here:

brainly.com/question/25813512

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