Question

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)

Answer 1

x=41.51

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,
`sin\theta=(perpendicular)/(hypotenuse)`

`sin49^(\circ)=(x)/(55)`

`0.754=(x)/(55)`

`x=0.754*55`

`x=41.509`

`x=41.51`

Answer 2

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