Simple angle relationship question

In summary, when given an angle in degrees and a relationship involving a constant and another angle, to find the second angle in degrees you can use the formula gamma = arctan ((24/13)*tan(theta)) or convert to radians first using gamma = arctan ((24/13)*tan(theta)) and then convert the resulting answer back to degrees.
  • #1
jx44
2
0
So I have a minor in mathematics yet I am confusing myself over the following - if I am given an angle, theta, in degrees and need to find a second angle, gamma, in degrees, and the relationship is tan(theta) = C*tan(gamma), where C is some constant, can I plug in theta in degrees and get gamma in degrees? Or do I need to convert theta to radians, find gamma in radians, then convert gamma to degrees again? If I do it with degrees I get 26.32, but if I do it the radians way i get 27.69.
 
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  • #2
Careful, that constant is going to be different if you're using radians or degrees or arcseconds or what have you, if you just bounce around units and use the same constant, you'll be wrong
 
  • #3
tan(15degrees)=(13/24)*tan(gamma)

gamma = arctan ((24/13)*tan(15 degrees))

gamma = 26.32
 
  • #4
Ah, but you got the answer in radians originally, didn't you? Then you had to convert it to degrees

tan(15 degrees)=tan(.261...) they're the outright same number, that value for C will always without fail give you the answer in radians, regardless of what you use in the input
 

Related to Simple angle relationship question

1) What are the different types of angles?

The three main types of angles are acute angles (less than 90 degrees), obtuse angles (greater than 90 degrees), and right angles (exactly 90 degrees).

2) How do I determine if two angles are complementary?

Two angles are complementary if their sum is equal to 90 degrees. For example, if one angle is 40 degrees, the other angle must be 50 degrees to be complementary.

3) What is the difference between adjacent and vertical angles?

Adjacent angles share a common side and vertex, while vertical angles are formed by two intersecting lines and are opposite from each other. In other words, adjacent angles are next to each other, while vertical angles are across from each other.

4) How do I find the missing angle in a triangle?

In a triangle, the sum of all angles is always equal to 180 degrees. So, to find a missing angle, you can subtract the known angles from 180. For example, if two angles in a triangle are 50 degrees and 70 degrees, the missing angle would be 60 degrees (180 - 50 - 70 = 60).

5) Can two obtuse angles be supplementary?

No, two obtuse angles (greater than 90 degrees) cannot be supplementary (equal to 180 degrees). The sum of two obtuse angles will always be greater than 180 degrees, making them unable to be supplementary.

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