Solving Sin & Cosin Law Homework | Find Angle Measure

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In summary, the question is asking for the measure of an acute angle, to the nearest tenth of a degree. The students used the sin and cosin laws to solve for the angle adjacent to theta in the left triangle, and then used that information to solve for angle opposite to the 100cm in the right triangle. However, they were still unable to get the answer correct.
  • #1
HelloMotto
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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 [Broken]

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.
 
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  • #2
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.
 
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  • #3
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?
 
  • #4
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.
 
  • #5
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)
 
  • #6
I'm getting frustrated on c). I really can't find any reason why 105.1[tex]^{o}[/tex] 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[tex]^{o}[/tex].
 
  • #7
for c) the diagram is probably wrong then. i don't see any reason for the angle opposite to 100cm to be an obtuse.
 
  • #8
question c is actually a ambiguous case lol. that's what i thought. thanks anyways helping me out.
 

What is the purpose of using the Sin and Cosin laws?

The Sin and Cosin laws are used to solve triangles when given specific information, such as side lengths and angle measures. These laws are helpful in finding missing angle measures, side lengths, and in proving congruence and similarity between triangles.

What is the difference between Sin and Cosin laws?

The Sin law, also known as the Law of Sines, is used to find missing angle measures and side lengths in any triangle. The Cosin law, also known as the Law of Cosines, is used to find missing side lengths and angle measures in triangles with a known angle and two known side lengths.

How do you use the Sin and Cosin laws to find angle measures?

To use the Sin and Cosin laws to find angle measures, you need to have at least one side length and its opposite angle measure. Plug this information into the appropriate law and solve for the missing angle measure using algebraic equations.

What happens if there is not enough information to use the Sin and Cosin laws?

If there is not enough information to use the Sin and Cosin laws, you will not be able to find the missing angle measure. In this case, you may need to use other methods, such as the Pythagorean theorem or other trigonometric functions, to find the missing information.

Can the Sin and Cosin laws be used to solve any triangle?

Yes, the Sin and Cosin laws can be used to solve any triangle, as long as you have enough information to apply the laws. However, keep in mind that there are other methods that may be more efficient in certain situations, so it is important to understand when to use the Sin and Cosin laws and when to use other methods.

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