What is the perimeter P of △DEF to the nearest whole number?

perimeter of ΔDEF  ≈ 32

Step-by-step explanation:

To find the perimeter of the triangle, we will follow the steps below:

First, we will find the length of the side of the triangle DE and FF

To find the length DE, we will use the sine rule

angle E  = 49 degrees

e= DF = 10

angle F = 42 degrees

f= DE =?

we can now insert the values into the formula

=  

cross-multiply

f sin 49° = 10 sin 42°

Divide both-side by sin 49°

f = 10 sin 42° / sin 49°

f≈8.866

which implies DE ≈8.866

We will now proceed to find side EF

To do that we need to find angle D

angle D + angle E + angle F = 180°  (sum of interior angle)

angle D + 49° + 42° = 180°

angle D + 91° = 180°

angle D= 180° - 91°

angle D = 89°

Using the sine rule to find the side EF

angle E = 49 degrees

e= DF = 10

ange D = 89 degrees

d= EF = ?

we can now proceed to insert the values into the formula

=  

cross-multiply

d sin 49° = 10 sin 89°

divide both-side of the equation by sin 49°

d= 10 sin 89°/sin 49°

d≈13.248

This implies that length EF = 13.248

perimeter of ΔDEF = length DE + length EF + length DF

                                  =13.248   +  8.866  + 10

                                   =32.144

                                    ≈ 32 to the nearest whole number

perimeter of ΔDEF  ≈ 32

14

step-by-step explanation: