Answer:
24 units
Step-by-step explanation:
From the description:
We also know that
sin(a) = 4/5
From definition:
sin(a) = opposite/hypotenuse
Replacing:
4/5 = EF/DE
EF = (4/5)*DE
EF = (4/5)*30 = 24 units
The length of the segment EF of the triangle DEF is 24 units.
In the image attached below we summarize the triangle described in statement, by trigonometric relationship we find that the length of the segment EF is described by the following expression:
[tex]\sin a^{\circ} = \frac{EF}{DE}[/tex] (1)
If we know that [tex]DE = 30[/tex] and [tex]\sin a^{\circ} = \frac{4}{5}[/tex], then the length of the segment EF is:
[tex]EF = DE\cdot \sin a^{\circ}[/tex]
[tex]EF = 30\cdot \left(\frac{4}{5} \right)[/tex]
[tex]EF = 24[/tex]
The length of the segment EF of the triangle DEF is 24 units. [tex]\blacksquare[/tex]
To learn more on right triangles, we kindly invite to check this verified question: https://brainly.com/question/7894175
