72.6k views
1 vote
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)

User Jayron
by
8.6k points

2 Answers

2 votes

Answer:

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



Use ΔDEF, shown below, to answer the question that follows: Triangle DEF where angle-example-1
User ZeroUnderscoreOu
by
7.9k points
5 votes
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

User Carles
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories