Find Angle in Right Triangle Given Hyp and Opposite Side

[vysero]

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?

 

[SteveL27]

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.

 

[vysero]

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.

 

[adriaat]

Anyway, the hypotenuse of a right triangle can't be never shorter than any cathetus, so you must have wrong lengths.

 

[vysero]

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.

 

[SteveL27]

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.

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.

 

[HallsofIvy]

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.