Question

solve each triangle. round each side length to the nearest tenth and angle measures to the nearest degree. a= 14, c= 20, B= 38 degrees.

Answer 1

Okay after scratching my head and some scrap paper :P I was really surprised to see that I don't remember ever running into this before...

Using the Law of Cosines we find the third side.

c=√(196+400-560cos38)≈12.4384 (we can round further for the final answer)

Now using the Law of Sines for the other angles.

sin38/12.4384=sinA/14=sinB/20

A=arcsin(14sin38/12.4384)≈43.8645°

BUT what I didn't realize before is that B was obtuse which means:

B=180-arcsin(20sin38/12.4384)≈98.135°

So solved for sides and angles (with rounding asked for)

(14, 44°), (12.4, 38°), and (20, 98°)

Answer 2

a) the missing degree is 166

b) the missing degree is 142

c)the missing degree is 160


I do hope I helped you in a way! If I am incorrect I apologize.