Solving Sin & Cosin Law Homework | Find Angle Measure

[HelloMotto]

Homework Statement

the question is

Find the measure of the indicated angle, to the nearest tenth of a degree.

Heres a picture of the question. (sorry for the bad quality)
http://img107.imageshack.us/img107/7002/mathproblem2bb2.jpg

ok for c) and d) I've applied what I've learned during the lesson, which was sin and cosin laws to try and solve this question...because this question is based on that lesson.

and I just can get the same answer as the answer in the back of the book.for c i got the answer of 105.4 degrees... which makes absolutely no sense because the unknown angle is a acute angle, and the actual answer is 20.6 degrees.

for d I got 1.9 degrees, but the actual answer is 7.8 degrees.

could somebody provide me with a step by step instruction on solving this problem please?

edit: for question d, the unknown angle is on the smaller triangle.

 

[pooface]

c)

sine law: sinA/a = sinB/b = sinC/c

use sine law to solve for the side adjacent to theta in the left triangle

then you can use sine law again to find angle opposite to the 100cm in the right triangle. then simple angle addition will tell you what theta is.

i can't see d) clearly. it is cut off.

 

[HelloMotto]

ok the side adjacent to the theta is 61.5 m. I then use that length to use it in my sin law equation to calculate that angle opposite to the 100 cm which was 47.9 degrees. i then added 47.9 with 27 and subtracted it from 180 and i got 105.1 degrees. still wroung answer:(

did i miscalculate something?

 

[kbaumen]

Well, perhaps the answer sheet has wrong answers. I also got the same results as you, Hello. But in that case either the diagram or the numbers given are wrong, because if theta is the widest angle, then it's opposite side should be the longest in that triangle.

 

[HelloMotto]

that could be one explanation.. i kind of doubt the books will have 3 incorrect answers for this question. The only question I've gotten right is a) which was 104.3 degrees. Does this question require more than the basic equation of sin and cosing law?

Or is this question a possible ambiguous case of sin law?(cause that's our next lesson...just curious)

 

[kbaumen]

I'm getting frustrated on c). I really can't find any reason why 105.1^{o} is not the answer.

P.s. In d) I think you should check your calculations again or show your calculations. I got to an answer ~8^{o}.

 

[pooface]

for c) the diagram is probably wrong then. i don't see any reason for the angle opposite to 100cm to be an obtuse.

 

[HelloMotto]

question c is actually a ambiguous case lol. that's what i thought. thanks anyways helping me out.