4. find the missing values of the special right triangles. simplify answers. **no decimals **
60*
5 ft
2 1cm
3.56 mi

1)m=9ft and n=10ft

2) p=10cm and r=18cm

3) s=4mi and t=8mi

Step-by-step explanation:

1)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides m and n

m/sinD = 5/sinF

m= sin60(5/sin30)

  = 8.66

   = 9

n/sinE= 5/sin30

n= sin90(5/sin30)

  = 10

hence m=9ft and n=10ft

2)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides p and r

p/sinF = 21/sinE

p= sin30(21/sin90)

  = 10.5

   = 10

r/sinD= 21/sin90

r= sin60(21/sin90)

  = 18.18

  =18

hence p=10cm and r=18cm

3)

Finding 3rd angle:

F= 180-(90+60)

 = 180-150

 =30

Now using law of sines to find sides s and t

s/sinF = 3√6/sinD

s= sin30(3√6/sin60)

  = 4.24

   = 4

t/sinE= 3√6/sinD

t= sin90(3√6/sin60)

  = 8.48

  = 8

hence s=4mi and t=8mi !