Find Angle in Right Triangle Given Hyp and Opposite Side

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SUMMARY

The discussion centers on calculating angles in a right triangle using the hypotenuse and the opposite side. A user mistakenly attempted to find an angle using the sine function with incorrect values, leading to confusion. The correct approach involves ensuring that the hypotenuse is always the longest side and that the sine of an angle must be between -1 and 1. Additionally, the conversation highlights the importance of verifying calculations and understanding basic mathematical principles, such as the relationship between circumference and radius.

PREREQUISITES
  • Understanding of right triangle properties
  • Knowledge of trigonometric functions, specifically sine
  • Familiarity with basic arithmetic operations
  • Ability to interpret mathematical relationships in geometry
NEXT STEPS
  • Study the properties of right triangles and the Pythagorean theorem
  • Learn how to use the sine, cosine, and tangent functions for angle calculations
  • Explore the relationship between circumference and radius in circles
  • Practice common sense checks in mathematical problem-solving
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This discussion is beneficial for students learning geometry, educators teaching trigonometry, and anyone seeking to improve their mathematical problem-solving skills.

vysero
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If I have a right triangle and I know the hyp and the length of the opposite side of the angle I want then how do I find that angle? For instance: hyp = .9m and side opposite the angle I want = 1.5m. I tried dividing 1.5/.9 = 1.7 then I thought all i had to do was take the inverse sin of 1.7 and it would give me my angle but my calc gives me an error... So I am confused, how do I get the angle i want?
 
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vysero said:
If I have a right triangle and I know the hyp and the length of the opposite side of the angle I want then how do I find that angle? For instance: hyp = .9m and side opposite the angle I want = 1.5m. I tried dividing 1.5/.9 = 1.7 then I thought all i had to do was take the inverse sin of 1.7 and it would give me my angle but my calc gives me an error... So I am confused, how do I get the angle i want?

Sine oscillates between -1 and 1 so you can't take the inverse sine of 1.7, right? You should probably draw a picture and make sure you've got the relationships right.
 
I figured out that it's not going to work like that because I am asking for a value greater than 1... ok so I acted to brashly and asked for help before I thought my question through sorry guys ignore this post.
 
Anyway, the hypotenuse of a right triangle can't be never shorter than any cathetus, so you must have wrong lengths.
 
Okay so here is the problem. If I have a circumference of .9m and I want the radius of the circle then I just divide .9 by 2pi right? Which according to my calculator = 1.5 m... However, when I put this same problem into Microsoft mathematics it says r = .14 When I look at the solution steps it says something about how dividing by 2pi undoes the multiplication of 2pi... I guess I am missing something here.
 
adriaat said:
Anyway, the hypotenuse of a right triangle can't be never shorter than any cathetus, so you must have wrong lengths.

Plus 1 for cathetus. I've only ever heard the word "leg" in this context. Good knowledge! And welcome to the forum.

vysero said:
Okay so here is the problem. If I have a circumference of .9m and I want the radius of the circle then I just divide .9 by 2pi right? Which according to my calculator = 1.5 m...

That can't be right. One little math trick is to always compare calculator results to common sense. That's a lifesaver on tests. As you work, continually make common-sense estimates and see if your numbers are in the ballpark.

Pi is about 3, right? That's close enough for the moment. So what's 2pi? It's about 6. And if I take .9 and divide by 6, how can the answer be 1.5? If I start with .9, which is a little less than 1; and I divide it into 6 pieces; then each piece needs to be way less than 1. Can't be greater than 1. So right here if you're thinking about this as you go, you'd know you made a mistake.

I apologize for being a dinosaur here ... but you should put down that calculator. You're punching numbers in as a substitute for thinking about what's going on. Easy to do. But it can lead you astray. Better to just work this problem out on paper.

By the way, 9 divided by 6 is 1.5. You forgot the decimal point. But if you develop the habit of doing reality checks as you work, you'll avoid these kinds of errors on tests.
 
Last edited:
vysero said:
Okay so here is the problem. If I have a circumference of .9m and I want the radius of the circle then I just divide .9 by 2pi right? Which according to my calculator = 1.5 m...
Then get a new calculator or reread the manual! A small number divided by a larger number (2pi is larger than 6) cannot be larger than 1. .9 divided by 2\pi is about .14. Surely you aren't under the impression that \pi= 0.314... but that would be my best guess- that you have drop a factor of 10.

However, when I put this same problem into Microsoft mathematics it says r = .14 When I look at the solution steps it says something about how dividing by 2pi undoes the multiplication of 2pi... I guess I am missing something here.
Uh, basic arithmetic? When you learn how to divide, in the second or third grade, you should learn that division is the reverse of multiplication.
 

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