solve the triangle:
1. A= 61 degrees
a=8
b=21
2. A=136 degrees
a=15
b=28
3. C=115 degrees
b=12
c=7
For all of these problems I used law of sins and when I input it into my calculator I get domain error after doing sin inverse to get an angle degree. What am I doing wrong?
These problems are made up to show some cases where the triangle cannot exist.
If A=61° (acute) and a=8, the longest side adjacent to A is a/sin(61°)=9.15.
Since 21>>9.15, the triangle does not exist.
If A is obtuse, then any adjacent side must be less than a.
Verify the above with a few triangles.
Okay, so all three of these are cases where the triangle does not exist?
I suggest you
1. verify if the triangles exist or not according to the two (different) conditions above.
2. try to draw the given triangle, if possible.
If you have doubts, you are welcome to post your answers/results for a check.
When using the Law of Sines to solve a triangle, you need to make sure that the values you use are appropriate for the formula. Specifically, for the Law of Sines, you need to have the measure of an angle opposite a known side length. Let's go through each case to see what might be going wrong:
1. A = 61 degrees, a = 8, b = 21:
To solve this, you can use the Law of Sines which states that a/sin(A) = b/sin(B) = c/sin(C), where A, B, and C are the measures of the angles, and a, b, and c are the lengths of the opposite sides.
To find angle B, you can use the formula:
sin(B) = (b * sin(A)) / a
sin(B) = (21 * sin(61)) / 8
B ≈ 77.00 degrees (approximately)
To find angle C, you can use the formula:
sin(C) = (c * sin(A)) / a
sin(C) = (c * sin(61)) / 8
You would need the value of side c to continue solving this triangle.
2. A = 136 degrees, a = 15, b = 28:
Again, you can use the same formula as above:
sin(B) = (b * sin(A)) / a
sin(B) = (28 * sin(136)) / 15
B ≈ 167.54 degrees (approximately)
However, you would also need the value of side c to solve this triangle.
3. C = 115 degrees, b = 12, c = 7:
In this case, you have the measure of an angle opposite the side length you want to find. You can rearrange the Law of Sines formula to solve for side a:
a = (b * sin(A)) / sin(B)
a = (12 * sin(115)) / sin(B)
Here, you would need to know the angle measure B to continue solving this triangle.
It's important to note that the Law of Sines might not be applicable in every situation. Sometimes, the given information might not be sufficient to solve the triangle, or there might be multiple possible triangle configurations leading to a domain error in your calculator.
If you're encountering a domain error while using the inverse sine function on your calculator, make sure that you're using the correct mode (degrees or radians) in your calculator settings. By default, most calculators are set to either degrees or radians. You can adjust the mode to match the unit of measurement given in the problem.
Additionally, if the domain error persists, double-check your arithmetic calculations to ensure they are accurate.