Is there a way to find the angles in a triangle if all I know is the length of the sides?

Question

all I need is a formula, or method. thank you!

Answer 1

Use the Law of Cosines. Given sides a, b, and c, with opposite angles A, B, and C, then

a^2 = b^2 + c^2 - 2 bc cos A

That will give you angle A, and you can repeat the procedure for angles B and C.

Answer 2

Law of cosines applies. Normally it is written as

c^2 = a^2 + b^2 - 2 a b cos C

where a, b and c are the sides and C is the angle opposte side c. Note that this formula is an extension of the Pythagorean theorem.

In your case, you know a, b and c and want to know C. Then

cos C = (a^2 + b^2 - c^2) / (2 a b)

take the inverse cosine and you have the angle. Other angles can be calculated the same way

cos A = (b^2 + c^2 - a^2) / (2 b c)
cos B = (c^2 + a^2 - b^2) / (2 c a)

For instance, if a = 10, b = 7 and c = 13 then

cos C = (7^2 - 10^2 - 13^2) / (2 * 7 * 10) = -20 / 140 = -1/7
so C = 108.2 degrees

cos A = (13^2 + 7^2 - 10^2) / (2 * 13 * 7) = 118 / 182 = 59/91
so A = 49.6 degrees

cos B = (10^2 + 13^2 - 7^2) / (2 * 10 * 13) = 220 / 260 = 11/13
so B = 32.2 degrees

Answer 3

Yes.
If there is a triangle ABC, with A, B, and C as the angles and a,b, c as the sides infront of each angle.
then the formula would be

cos A = ( b^2 + c^2 - a^2) / 2.b.c

cos B = ( a^2 + c^2 - b^2) / 2.a.c

from cosA, cos B, or cos C you can find how big the angle is

it comes from the original formula to find the lengths of 1 side with knowing 2 other sides and an angle across the side which length we dont know.

a^2 = b^2 + c^2 - 2.b.c.cos A

For example if we know that b is 4 and c is 3 and the angle of A is 60 degrees

a^2 = b^2 + c^2 - 2.b.c.cos A
a^2 = 16 + 9 - 2.4.3. cos 60
a^2 = 16 + 9 - 12
a^2 = 13
a = sq root of 13

Hope this helps...

Answer 4

in case you take advantage of the pythagorean theorem, that's amazingly simple. A^2 + B^2 = C^2. that's in case you want to reveal your paintings. yet keep in concepts, there are some excellent triangles that you'll be able to memorize and in no way ought to do the paintings. listed here are a pair: If the perimeters of a triangle are multiples of three and four (ie 6,8), then the hypotenuse is the corresponding assorted of 5. also, if the perimeters lengths are 5 and 12, a similar rule applies for 13.

Answer 5

There is. There are a number of formulas; one such is:
cos A = (c^2+b^2-a^2)/2bc. A handy shortcut: see if Pythagoras applies; if so, then it is a right triangle and the angles can easily be computed using sines and cosines.

Answer 6

if d triangle is equilateral den all angles are 60 degrees. if its a right angled triangle, den d longest side is 90 while d rest is 45. otherwise, i dont think u find d angles, an angle must be given 2 use d sine rule or cosine rule.

Answer 7

Yes, use the Law of Cosines:
a^2=b^2+c^2-2bc*cos(A)
where a,b, and c are the sides and angle A is opposite the side a.
If you have a,b, and c, it is easy to solve for cos(A) and hence for A.

Answer 8

yes ofcourse

You can use sine rule, u need to rearange the formula to get the sin(x) value, and use the sign inverse button on your calculator to find the angel

Answer 9

c^2 = a^2 + b^2 - 2ab(cosC)
becomes
c^2 - (a^2 + b^2) = -2ab(cosC)
(-1/2)(c^2 - (a^2 + b^2))/(ab) = cosC

A = cos^-1((-1/2)(a^2 - (b^2 + c^2))/(bc))
B = cos^-1((-1/2)(b^2 - (a^2 + c^2))/(ac))
C = cos^-1((-1/2)(c^2 - (a^2 + b^2))/(ab))

Answer 10

use sine rule and/or cosine rule