Riversongirl
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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.


Please explain your answer.

Respuesta :

DeanR

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.

[tex]\sin F = \dfrac{\textrm{opp}}{\textrm{hyp}} = \dfrac{DE}{DF}[/tex]

[tex]x = DE = DF \sin F = 55 \sin 49^\circ = 41.50902...[/tex]

Answer: 49.51

Cricetus

Answer:

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

[tex]sin \theta = \frac{perpendicular}{Hypotenuse}[/tex]

Perpendicular = DE

Hypotenuse = DF = 55

[tex]\theta=49[/tex] Degrees

[tex]sin 49= \frac{DE}{55}[/tex]

We use trigonometric calculator and find sin 49° = 0.75

Hence we have

[tex]0.75= \frac{DE}{55}[/tex]

DE= 55*0.75

DE=41.509 units

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