Angles

girlnamedfreak · 2006-11-19 03:35:46

how do you find the other two angles of a right triangle when you are given all the side lengths?

John E. Franklin · 2006-11-19 03:46:20

If you are sure it is a right triangle, then you only need to know 2 of the side lengths to get angles.
Use inverse cosine, inverse tangent, inverse sine, also known as arc cosine, arc tangent, arc sine.
If it is not a right triangle, I'm sure you need 3 sides, and there are formulas like "law of sines" and "law of cosines"

For a right triangle, one way, is to put the big leg flat along like a floor.
Then the tiny leg points upward like a wall.
You don't have to put the big one flat and the little leg upright, but I thought it would be interesting to try it.
...

John E. Franklin · 2006-11-19 03:51:09

Now the smallest angle of the 3 angles is the inverse tangent of small leg divided by the big leg.
And the middle-sized angle of the 3 angles is the big leg divided by the small leg, and tan-1 that.

tan-1 and arctan are inverse tangent.

-1
tan

Now the smallest angle plus the middle-sized angle add up to the same as the biggest angle, which is 90 degrees.

...

John E. Franklin · 2006-11-19 04:02:17

Let's take an example.
Say small leg is 10mm, and big leg is 90mm, and therefore the big side on a slant is 10 times 10 plus 90 times 90 and take the square root of that. So 10 times 10 is 100 and 90 times 90 is 8100, so add them together and you get 8200, and take the square root of 8200, and I need a calculator, be back.

Okay, the square root of 8200 is about 90.55~.

So you have a right triangle with legs 10mm and 90mm and long slanted side is 90.55~.

So now you know automatically that the right angle is 90 degrees and is between the two legs.

Now the angle between the 90mm and the 90.55~mm is the inverse cosine of 90 divided by 90.55~.

This is about 6.3~ degrees.

Now the angle between the 10mm and the 90.55~mm is the inverse cosine of 10 divided by 90.55~.

This is about 83.6~ or 83.7~ degrees.

You don't need to use the inverse sine if you don't want to, but you can learn it if you want.

...

mathsyperson · 2006-11-19 05:13:29

As John says, to find angles in a triangle having been given sides, you need to use trigonometry.

A
|\
| \
| \ c
b | \
| \
| \
----------- B
a

So here's your triangle. You know that sides a and b make a right angle, and you know all the lengths, and you want to find out the values of angles A and B.

Well, because you've been given all of the side lengths, you've got a lot of choices!

The 3 trigonometric rules are:

sinθ = opposite/hypotenuse
cosθ = adjacent/hypotenuse
tanθ = opposite/adjacent

So that means that you can work out either sin A, cos A or tan A by doing a/c, b/c or a/b respectively.

Once you've got that, you'll probably want to put that into a calculator and use the appropriate function out of sin[sup]-1[/sup], cos[sup]-1[/sup] or tan[sup]-1[/sup]. There are some occasions when you can work it out without a calculator, but you will usually need one, so it's easier to just use the calculator all the time. And once you've done that, you have your value for angle A.

You could then do the same thing for B, or you could recognise that A, B and the right-angle will all add to 180[sup]o[/sup] and so just use the value of A to deduce B. If you're not sure that your answers are right, then finding B both ways and making sure that the answers match is a good check.

girlnamedfreak · 2006-11-19 06:59:45

Thanks guys! Youre very helpful and get it now. The answers I got were correct because all the angles added up equal 180.

Math Is Fun Forum

#1 2006-11-19 03:35:46

Angles

#2 2006-11-19 03:46:20

Re: Angles

#3 2006-11-19 03:51:09

Re: Angles

#4 2006-11-19 04:02:17

Re: Angles

#5 2006-11-19 05:13:29

Re: Angles

#6 2006-11-19 06:59:45

Re: Angles

Board footer