SOLUTION: Is there a ratio relationship between the two small angles and the two shorter sides on a right angle triangle so that if I know the two angles and the length of one side I can fin

Algebra ->  Triangles -> SOLUTION: Is there a ratio relationship between the two small angles and the two shorter sides on a right angle triangle so that if I know the two angles and the length of one side I can fin      Log On


   

Question 541745: Is there a ratio relationship between the two small angles and the two shorter sides on a right angle triangle so that if I know the two angles and the length of one side I can find the second side. A simple ratio doesn't seem to work, unless I'm doing it wrong.
Thank You,
Bruce
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In a right triangle, if you know which angle is the right angle, and you know the measure of just one of the smaller angles, you really know two angles. You can calculate the measure of the other angle, because you know (or will after you read this) that the sum of the measures of the angles of a triangle is always 180 degrees.
If you also have the length of a side, you can find the lengths of the other two.
I'll refer to the drawing at left as I explain everything there is to know about right triangles.
To begin, convention says that the angles are named with capital letters, and the same letter, but in lowercase is used to label the side directly opposite each angle. In my drawing, I labeled the right angle C. The side directly opposite the right angle (c) is called the hypotenuse. The other two sides are called legs. The legs of a right triangle are shorter than the hypotenuse.
The ratios of the lengths of the sides of a right triangle are related to the measures of the smaller angles by the trigonometric ratios, that do not change if the triangle is made larger or smaller without changing the angles.
The trigonometric ratios to remember are:
sin%28angle%29=opposite%2Aside%2Fhypotenuse (Sine=Opposite/Hypotenuse)
cos%28angle%29=adjacent%2Aside%2Fhypotenuse (Cosine=Adjacent/Hypotenuse)
tan%28angle%29=opposite%2Aside%2F%28adjacent%2Aside%29 (Tangent=Opposite/Adjacent)
Teachers try to help students remember by using the capitalized first letters of the words in parentheses above to make the nonsense word SOHCAHTOA.
In the triangle in my drawing:
sin%28A%29=a%2Fc sin%28B%29=b%2Fc
cos%28A%29=a%2Fc cos%28B%29=b%2Fc
tan%28A%29=a%2Fb tan%28A%29=b%2Fa
I do not know why what you are doing is not working. Maybe you can give me more details. If you put them in the form of the thank you notes the website has, I'll get the information. If you post it as one more problem in the fast flowing stream, I will most probably miss it, but maybe some one else will help.
I'll add more to this post later, anyway. I've got to go to the job that pays now.