Question

find the interior angles of the triangle with vertices A(0,5) B(2,1) C(-2,-1)

Answer 1

First here's a graph:

Answer 2

So do you know the distance formula? I think this might be a good place to start.

Answer 3

I think that if you used 2 of the points and used the distance formula you could find the length of one side of triangle. Once you repeated this you could then pick an angle and use inverse sin or cos or tan to find the angle that represents that ratio.

Answer 4

Find the lengths of AB, BC and AC.
Unless the triangle is a right triangle you can use the law of cosines to find the angle:
BC^2 = AB^2 + AC^2 - 2(AB)(AC)cos(A)
Knowing three sides, plug in and solve for A.
Find B in a similar way.
Then C = 180 - (A + B)

Answer 5

You can also find the slopes of each line, take arctan, find the angle each line makes with the x-axis, subtract them to find the angle between the sides.

Answer 6

Line AC² = 6² + 2²
Line AC² = 40
Line AC = 6.3245553203

Line AB² = 4² + 2²
Line AB² = 20
Line AB = 4.472135955

Line BC² = 2² + 4²
Line BC² = 20
Line BC = 4.472135955

Line AB = BC so ABC is an isosceles triangle and if ABC is a right angle then triangle ABC is a right isosceles triangle ( a 45 45 90 triangle).

Does AB² + BC² = AC²
Yes, and so triangle ABC is a 45 45 90 triangle and the angles are 45° 45° and 90°.

Answer 7

there is a mathematical error @ranga

Answer 8

@ranga

Answer 9

there is undefined in TAN B

Answer 10

@jacalneaila Not sure the mathematical error to which you were referring.
I am getting the same answers as wolf1728.
BC^2 = AB^2 + AC^2 - 2(AB)(AC)cos(A)
20 = 20 + 40 -2sqrt(20)sqrt(40)cos(A)
cos(A) = 40/(2sqrt(20)sqrt(40)) = sqrt(40)/(2sqrt(20)) = 1/sqrt(2)
A = 45 degrees.
Since AB^2 = BC^2; AB = BC
Therefore, C = 45 and B = 90.

Answer 11

Oh you are getting undefined because one of the angles happen to be 90 degrees and tan(90) is undefined.
If you are using the slope method ignore that angle and use the arctan(slope) to find the other two angles. Each will come out to be 45 degrees. Then subtract 180 - 45 - 45 to get angle B.

Answer 12

Too faint or out-of-focus to read.

Answer 13

Looks like you got the two 45 degrees. Knowing two angles of a triangle you can find the third angle. Just don't use the slope method if one of the angles happen to be 90 degrees.

Answer 14

Tan b is undefined T.T @ranga

Answer 15

Yes. That is because B = 90 degrees. tan(90) = infinity.