Answer:
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 !
