Trigonometry angle - calculation failed, can't explain.

In summary, the student attempted to solve for angle A using the laws of sines, but ended up with an error because the angle A was larger than expected. Next, the student solved for angle B using the same laws of sines and found that it was adjacent to angle C. From there, the student was able to solve for angle C using the same laws of sines.
  • #1
Monocerotis
Gold Member
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0

Homework Statement


I have to find the measures of the angles x & y.

2mwtkc6.jpg


Homework Equations


Sine Law
Cosine Law


The Attempt at a Solution




First thing I tried to do was find the measure of the angle @ A.

a/SinA = c/SinC
66/SinA = 25/Sin10.5

and then I end up with 28 degrees for the angle @ A. 28 degrees is obviously wrong. I'm ending up with an error and I can't understand why because so far as I understand my procedure is correct.

I want to solve for angle A, then because I already have angle C I can solve for angle B.

From angle B I could find the angle next to (x), thereby finding x becasue the sum of the two would be 180.
 
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  • #2
Your picture is way out of scale and is misleading you. Angle A is actually much larger, angle C much smaller, and line AB much shorter than in your picture. Remember the law of sines can give two solutions and this is one of those cases. Your calculation for angle A is actually giving you the supplement of angle A. Subtract it from 180 to get angle A. Redraw your picture more to scale and you will see.
 
  • #3
LCKurtz said:
Remember the law of sines can give two solutions and this is one of those cases. Your calculation for angle A is actually giving you the supplement of angle A. Subtract it from 180 to get angle A. Redraw your picture more to scale and you will see.

Thanks man, I didn't know that law of sines can give you two solutions, we just started our trig unit last class.

So just to be sure, for future assignments or whatever, I would work out the question like this.

Sin C/c = Sin B/b

Sin 10.5/25 = Sin B/66

(66)Sin10.5/25 = Sin B
Sin^-1(0.4811) = B
28.75 = B

180 - 28.75 = B
151.25 = B

and then work out the rest of the triangle, which is much easier

is that the correct method ?
 
  • #4
Given triangle with angles ABC with sides a,b,c opposite, suppose you know angle A, side b and side a. If you use the law of sines to find angle B, there will be two solutions whenever a is between b and b sin(a): b > a > b sin(A).

If b is outside that range there will be only one solution. You don't always take the supplement.
 

Related to Trigonometry angle - calculation failed, can't explain.

1. Why did the trigonometry angle calculation fail?

There could be several reasons for a trigonometry angle calculation to fail. Some common reasons include incorrect input values, using the wrong formula or equation, or missing a step in the calculation process. It is important to double check all input values and follow the correct steps to ensure a successful calculation.

2. How can I fix a failed trigonometry angle calculation?

If your trigonometry angle calculation has failed, the best way to fix it is to review your steps and make sure all input values are correct. If you are using a calculator, ensure that it is set to the correct mode (degrees or radians) and that you are using the correct buttons and functions. If you are still having trouble, it may be helpful to seek assistance from a teacher or tutor.

3. Can you explain the concept of trigonometry angles?

Trigonometry angles are a fundamental part of trigonometry, which is the study of triangles and their properties. An angle in trigonometry is formed by two intersecting lines and is measured in degrees or radians. Trigonometry angles are used to calculate the sides and angles of a triangle, as well as in many real-world applications such as navigation, engineering, and physics.

4. What are some common uses for trigonometry angles?

Trigonometry angles have many practical uses in fields such as engineering, physics, and navigation. They are used to calculate distances, heights, and angles in real-world scenarios. For example, they are used in surveying to measure land and in architecture to design and build structures. They are also crucial in understanding and solving problems involving waves, vibrations, and oscillations.

5. How can I improve my understanding of trigonometry angles?

To improve your understanding of trigonometry angles, it is important to practice solving problems and working through examples. You can find many resources online, such as tutorials, practice problems, and interactive quizzes, to help you gain a better understanding of the concepts. It can also be helpful to seek guidance from a teacher or tutor who can provide personalized instruction and assistance.

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