Question

In right triangle DEF, FE=5 and angle F=40°. Find DE to the nearest tenth.

Answer 1

Draw out the triangle DEF, FE would be the hypothenuse, angle F would be one of the base angles, and DE is the opposite side length. To find the length of DE, use trig so 5 • sin 40 = 3.7

Answer 2

For this case, we have that by definition:

`Sine (A) = \frac {Cathet \ opposite \ a \ A} {Hypotenuse}`

So:

`Sine (F) = \frac {DE} {FE}`

We have to:

`F = 40 \ degrees\\FE = 5`

Substituting:

`Sine (40) = \frac {DE} {5}\\DE = Sine (40) * 5\\DE = 0.64278761 * 5\\DE = 3.21393805`

Rounding:

`DE = 3.2`

Answer:

`DE = 3.2`