Calculate angle of triangle Python

Question

I'm trying to find out the angle of the triangle in the following, I know it should be 90 degrees, however I don't know how to actually calculate it in the following:

enter image description here

Here's what I've tried:

angle = math.cos(7/9.899)
angleToDegrees = math.degrees(angle)

returns: 43.XX

What am I doing wrong?

This gives the angle between A and C. Look into the law of cosines. — Teepeemm, Sep 03 '13 at 02:34
If I were to use `tan` I get closer... `x = math.tan(7/7)` and then `math.degrees(x)` returns `89.2328896038`? why isn't this an even 90? — Shannon Hochkins, Sep 03 '13 at 02:37
A single trigonometric function will only work if you already have a right angle in the triangle, and are trying to find a different angle. `math.tan` takes radians and gives a ratio. `math.degrees` takes radians and gives degrees. They giving you almost 90 is coincidental. — Teepeemm, Sep 03 '13 at 03:26
all of the trig functions convert between an angle and the ratio of two sides of a triangle. cos, sin, and tan take an angle in radians as input and return the ratio; acos, asin, and atan take a ratio as input and return an angle in radians. You only convert the angles, never the ratios. — Neo Ravi, Apr 14 '18 at 11:56
As @Teepeemm explains, the ratio leg1/hypotenuse gives you the cosine of the angle adjacent to leg1 that is NOT the right angle. In this case, because the triangle is isosceles, 45 degrees. — InverniE, Mar 10 '19 at 13:31

score 23 · Accepted Answer · edited Dec 11 '16 at 09:48

23

It's a little more compicated than that. You need to use the law of cosines

>>> A = 7
>>> B = 7
>>> C = 9.899
>>> from math import acos, degrees
>>> degrees(acos((A * A + B * B - C * C)/(2.0 * A * B)))
89.99594878743945

This is accurate to 4 significant figures. If you provide a more precise value of C, you get a more accurate result.

>>> C=9.899494936611665
>>> degrees(acos((A * A + B * B - C * C)/(2.0 * A * B)))
90.0

edited Dec 11 '16 at 09:48

Vibert Thio

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answered Sep 03 '13 at 03:02

John La Rooy

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That worked great, you wouldn't mind explaining it a bit more though would you? – Shannon Hochkins Sep 03 '13 at 03:12
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@ShannonHochkins, follow the link to wikipedia for the explanation. It's really off-topic for this site. – John La Rooy Sep 03 '13 at 03:13
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Why is it off topic? I asked how to calculate this, usually an answer is best when it has better descriptions rather than just the code. – Shannon Hochkins Sep 03 '13 at 07:16
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@ShannonHochkins, because it's math. You could try asking for an explanation on math.stackexchange.com – John La Rooy Sep 03 '13 at 07:39

score 3 · Answer 2 · edited Aug 12 '19 at 10:10

3

You can use this also.

print(str(int(round(math.degrees(math.atan2(x,y)))))+'°')

This accepts two inputs as two heights of the triangle and you can get the output angle in proper degree format.

edited Aug 12 '19 at 10:10

Suraj Rao

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answered Aug 12 '19 at 10:05

himanshu

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score 0 · Answer 3 · answered Sep 03 '13 at 02:36

0

i think you're looking for math.acos not math.cos, you want to return the angle whose value is the ratio of those two sides. not take its cosine.

answered Sep 03 '13 at 02:36

yoshi

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This just gave me an even 45.00 – Shannon Hochkins Sep 03 '13 at 02:41
Trig functions are for when you have an angle of 90 degrees, and you're interested in some other angle. – Teepeemm Sep 03 '13 at 14:07
@Teepeemm trig funcs are for all triangles, they are just simpler when a 90deg angle is involved. – TehTris Sep 03 '13 at 17:49

score 0 · Answer 4 · answered Sep 03 '13 at 02:52

0

Trig functions will convert an angle into a length of a certain leg of a certain triangle. In particular, the tangent is the ratio of the opposite side to the adjacent side. math.tan(7/7) is the length of the right triangle opposite an angle of 1(=7/7) radian. This length (~1.557) just happens to be near to the number of radians which is 90 degrees (pi/2 ~ 1.571).

As noted, you're looking for an inverse trig function to convert a length back into an angle.

answered Sep 03 '13 at 02:52

colcarroll

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is that not what math.degrees does? converting radians to degrees/angles – Shannon Hochkins Sep 03 '13 at 02:57
It does convert radians to degrees. But tan(1) is not radians to begin with. The fact that you are treating it as radians is wrong. – Teepeemm Sep 03 '13 at 14:10

score 0 · Answer 5 · answered Apr 29 '18 at 15:02

0

use this:

import math
AB = float(input())
BC = float(input())

print(str(int(round(math.degrees(math.atan2(AB, BC)))))+'°')

answered Apr 29 '18 at 15:02

HasanShovon

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This code assumes that OP's marked angle is 90degrees, and then gives the acute angle next to input "BC". – Teepeemm Mar 10 '19 at 22:17

Calculate angle of triangle Python

5 Answers5