Use △def, shown below, to answer the question that follows: triangle def where angle e is a right angle. de measures x. df measures 55. angle f measures 49 degrees. what is the value of x rounded to the nearest hundredth? type the numeric answer only in the box below. explain your answer.

We're told E is right and we're given DF, the hypotenuse. We seek x=DE, the side opposite vertex F.

We have opposite and hypotenuse; that's sine.

49.51

DE= 3.75 units

Step-by-step explanation:

Here we are given a right triangle Δ DEF right angled at E.

We are given that ∠EFD=49°

and DF = 55

DF is our hypotenuse .

Here we have to find the value of DE.

In order to do so , we will use trigonometric ratios

We know that

Perpendicular = DE

Hypotenuse = DF = 55

Degrees

We use trigonometric calculator and find sin 49° = 0.75

Hence we have

DE= 55*0.75

DE=41.509 units

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