Question

A triangle was dilated by a scale factor of 6. If sin aº

- and De measures 30 units, how long is EF?

EF = 15.5 units

EF = 24 units

EF = 30 units

EF = 37.5 units

PLEASE HELP

Answer 1

EF= 24 units

Explanation:

I took the test and it was right

Answer 2

24 units

Explanation:

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

From the description:

angle D measures a degrees

opposite to angle D is side EF

side DE (which measures 30 units) is the hypotenuse of the triangle.

We also know that

`\sin (a) = (4)/(5)`

`\sin (a) = (opposite)/(hypotenuse)`

From definition:

`\sin (a) = (opposite)/(hypotenuse)`

Replacing:

`(4)/(5) =( EF)/(DE) \\\\EF = (4)/(5) *DE\\\\EF = (4)/(5) *30 \\\\= 24 units`