Solving Triangles. My answer fluctuates from the real answer

[Tyler2358]

Hey Guys. I'm having a bit of a problem with my solving triangles book. I'm finding the book really easy but there's this one thing that I keep getting wrong. Whenever I'm working with degrees with decimal points my answer aways fluctuates slightly from the real answer. I must be doing something wrong. Any help will be greatly appreciated!

 

[Mentallic]

I'm getting 8.62. Can you show me your input into your calculator? How are you expressing the minutes for example?

 

[Mentallic]

Actually, I see what you've done. You expressed $65^o5'$ as 65.5 in your calculator. This is not correct!

$$65.5^o=65^o30'$$

because $0.5^o$ is half of a degree, and that is equal to 30' since $60'=1^o$.

The opposite angle $24^o55'$ is NOT to be expressed as 24.55 in the calculator, but rather 24+55/60. Think about it in terms of time. The degree is the hour and the minute is the minute. What is 4 lots of 2 hours and 5 minutes equal to? Obviously it'll be 8 hours and 20 minutes. Let's check it though:

It's not 2.5*3 = 7.5, but rather 2 hours * 3 + 5/60 hours * 3 = 6 hours + 15/60 hours = 6 hours and 15 minutes.

This is what you want to put into your calculator:

$$\sin(65+5/60)*9.51$$

if your calculator is expressed in degrees.

 

[Tyler2358]

I'm getting 8.62. Can you show me your input into your calculator? How are you expressing the minutes for example?

I did think maybe I'm calculating the minutes wrong but for the life of me I couldn't find anything on the internet about it.

 

[Tyler2358]

Oh I see now. Thank you for helping me! Finally I've been stuck here for a while now.

 

[Mentallic]

You're welcome!

Also keep in mind that your calculator might also have a degrees, minutes and seconds button. You can use this button to easily express the degrees and minutes with $65^o5^o$ on the calculator, which would be equivalent to $65^o5'=65+5/60$. Also, if you start using seconds too, then
$$65^o5^o20^o$$ on your calculator would be equivalent to $$65^o5'20''=65+5/60+20/60^2=65+5/60+20/3600$$

 

[SteamKing]

I did think maybe I'm calculating the minutes wrong but for the life of me I couldn't find anything on the internet about it.

It's always going to be in the last place you look:

http://en.wikipedia.org/wiki/Degree_(angle)

 

[LCKurtz]

Little details like that are what makes space probes fail to go into orbit around Mars.