Question

4. Find the missing values of the Special Right Triangles. Simplify answers. **no decimals **

60*
5 ft
2 1cm
3.56 mi​

Answer 1

1)m=9ft and n=10ft

2) p=10cm and r=18cm

3) s=4mi and t=8mi

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 !