Question

Triangle D E F is shown. Angle D E F is 90 degrees and angle F D E is 42 degrees. The length of D E is 7.2 and the length of E F is d. What is the value of d to the nearest hundredth? d ≈

Answer 1

6.48

Explanation:

just did the test

Answer 2

The value of the d is 6.48, if the angle D E F is 90 degrees and angle F D E is 42 degrees and the length of D E is 7.2 and the length of E F is d.

Explanation:

The given is,

Angle D E F is 90 degrees

Angle F D E is 42 degrees

The length of D E is 7.2

The length of E F is d

Step:1

For the given values,

Triangle DEF is right angle triangle,

Ref the attachment,

Angle FDE, ∅ = 42°

DE = 7.2

EF = d

Trigonometric ratio for the given right angle triangle,

`tan` ∅ =
`(Opp)/(Adj)`

`tan` ∅ =
`(EF)/(DE)`

`tan 42 = (d)/(7.2)`

( the value of tan 42° = 0.900404 )

`(0.900404)(7.2)= d`

`d=6.48`

EF = d = 6.48

Result:

The value of the d is 6.48, if the angle D E F is 90 degrees and angle F D E is 42 degrees and the length of D E is 7.2 and the length of E F is d.