Question

laws of Sines special cases. Find each measurement. Round your answer to the nearest tenth. Part 1. Please show your work. #1-4​

Answer 1

1. No triangle formed

2. 41.5°

3. No triangle formed

4. 35.9°

Explanation:

1. a/sinA = c/sinC

24/sin70 = 28/sinC

sinC = 1.096308058

Triangle not possible

2. c/sinC = b/sinB

33/sin40 = 34/sinB

sinB = 0.6622660221

B = 41.47292235

3. b/sinB = c/sinC

26/sinB = 6/sin29

sinB = 2.100841688

Triangle not possible

4. a/sinA = c/sinC

16/sin28 = 20/sinC

sinC = 0.5868394535

C = 35.93304554

Answer 2

Apply sine theorem:

1.

c/sinC = a/sinA

=> sinC = sinA x (c/a) = sin70 x 28/24 = 1.096 => Invalid ( 1.096 > 1)

=> C is undefined

=> B is undefined

2.

c/sinC = b/sinB

=> sinB = sinc x (b/c) = sin40 x 34/33 = 0.662

=> B = arcsin(0.662) = 41.47 deg

3.

c/sinC = b/sinB

=> sinB = sinC x (b/c) = sin29 x 26/6 = 2.101 => Invalid ( 2.101 > 1)

=> B is undefined

=> A is undefined

4.

c/sinC = a/sinA

=> sinC = sinA x (c/a) = sin28 x 20/16 = 0.587

=> C = arcsin(0.587) = 35.93 deg

Hope this helps!

:)