Oh great lj overmind: Who's good at math?

06:09 pm July 16th, 2012




			Cheerfully Demented - Oh great lj overmind: Who's good at math?

frankwu


	Oh great lj overmind: Who's good at math?
	If only I remembered my high school geometry better.... If I have a right triangle, and I know the exact length of the two sides where are not the hypotenuse, how do I figure out the exact angles of the two sides which are not the right angle? Assume I do not have a trig calculator. Oh please someone help me!

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	From: del_c	Date: July 16th, 2012 10:12 pm (UTC)		(Link)

ARCTAN

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	From: del_c	Date: July 16th, 2012 10:17 pm (UTC)		(Link)

Oh, you don't have a calculator or Excel. Have you got any old tables on your bookshelf? CRC Handbook?

(You say you. Is it actually you, or a character you want to have solve this problem?)

Is one of the sides very very small? Then the small angle is about the ratio of the sides in radians. pi radians is 180 degrees, making a radian about 57 degrees.

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	From: daveon	Date: July 16th, 2012 10:16 pm (UTC)		(Link)

You need to know how to use the Sin, Cosine and Tangent buttons on a scientific calculator.

Draw the triangle, label the hypotenuse H, identify the angle you want to find, put a symbol in there. Label the side leading from the angle A (adjacent) and the one opposite that (O)

Then you can find the angles from the following formula:

Sin (angle) = Opposite / Hypotenuse

Consine (angle) = Adjacent / Hypotenuse

Tangent (angle) = Opposite / Adjacent

If memory serves because they're rations the units don't really matter.

It's been a few years since I did this crap, but I'm pretty sure that's what you need.

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	From: daveon	Date: July 16th, 2012 10:18 pm (UTC)		(Link)

Oh, and when you've got the adjacent angle, then the other angle is 180 - angle - 90...

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	From: daveon	Date: July 16th, 2012 10:19 pm (UTC)		(Link)

Oh, no Trig calculator? er... ah... find a set of trig tables on line?

http://www.themathlab.com/toolbox/geometry%20stuff/trigratios.htm

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	From: frankwu	Date: July 16th, 2012 10:22 pm (UTC)		(Link)

Excellent. Excellent. Thanks to both of you. This is great!

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	From: del_c	Date: July 16th, 2012 10:36 pm (UTC)		(Link)

You have a pencil, paper, a ruler marked with lengths, a compass (the drawing kind, not the magnetic kind) and some string.

Draw your triangle using the ruler, draw the arc from the right angled corner to the hypotenuse (with the compass centred on another corner), and use the string to measure the length of the arc. Divide the length of the string (i.e. the arc length) by the width of the compass (i.e. one of the sides), using long division with a pencil and paper. The ratio, again, is the angle in radians.

Notice why this all becomes unnecessary when the arc becomes tiny: it approaches the length of the other side.

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