A triangle was dilated by a scale factor of 6. If sin a° = four fifths and segment DE measures 30 units, how long is segment EF? triangle DEF in which angle F is a right angle, angle D measures a degrees, and angle E measures b degrees
15.5 units
24 units
30 units
37.5 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:

(1)

If we know that and , then the length of the segment EF is:

The length of the segment EF of the triangle DEF is 24 units.

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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

5

step-by-step explanation:

2: 10

step-by-step explanation: