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Use ΔDEF, 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. (4 points)

Respuesta :

You are given the hypotenuse and angle F, DE is the leg opposite to angle F, so use sin to solve this problem.
sinF=DE/DF
DE=DF*sinF=55*sin49=41.51

Answer:

x=41.51

Step-by-step explanation:

Given : ΔDEF, where angle E is a right angle, DE measures x, DF measures 55 and angle F measures 49 degree.

Since it is a right angle triangle,

Perpendicular DE=x, hypotenuse DF=55 and ∠F=49°

Refer the attached graph.

We know, [tex]sin\theta=\frac{perpendicular}{hypotenuse}[/tex]

[tex]sin49^{\circ}=\frac{x}{55}[/tex]

[tex]0.754=\frac{x}{55}[/tex]

[tex]x=0.754\times55[/tex]

[tex]x=41.509[/tex]

[tex]x=41.51[/tex]

 



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