Mathematics College

What is the length of segment DF?
B
4/28
1
68°
C
2
А A
2
3
8
4
68°
28°
F
5
Type your answer.

What Is The Length Of Segment DF?B4/28168C2 A23846828F5Type Your Answer.

Answers

Answer 1

Answer:

DF = 17.12

Step-by-step explanation:

From the picture attached,

From ΔABC and ΔEFD,

m∠ABC = m∠EFD = 28°

m∠BAC = m∠EDF = 68°

By AA property of similarity, ΔABC and ΔEFD will be similar.

And their corresponding sides will be proportional.

[tex]\frac{AB}{EF}=\frac{BC}{DF}=\frac{AC}{ED}[/tex]

[tex]\frac{4}{EF}=\frac{BC}{DF}=\frac{2}{8}[/tex]

[tex]\frac{4}{EF}=\frac{1}{4}[/tex]

EF = 16

Now by applying cosine rule in ΔDEF,

DF² = ED² + EF² - 2(ED)(EF)cos(E)

DF² = 8² + (16)² - 2(8)(16)cos(84)°

DF² = 320 - 26.76

DF = √(293.24)

DF = 17.12

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Answers

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Answers

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Step-by-step explanation:

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