math

posted by .

given the points A(0,0), B(3,1) and C (1,4)
what is the measure of angle ABC
I plotted it on a gragh and got
1.46 degress. I am unsure if I am doing this question correctly. Or am I misreading it

• math -

A simple sketch will show you that that answer cannot possibly be right

Extend CB to cut the x-axis at D
(using the basic concept that if the slope of a line is m and the line forms an angle of Ø with the x-axis
then tanØ = m)

slope of AB = 1/3
slope of CB = -3/2 , angle is obtuse
tan (angle of line with x-axis) = 123.69°
so angle BDA = 56.304°
and angle ABC is the exterior angle
and angle ABC = angle BAD + angle BDA
= 18.43° + 56.304° = 74.74°

or

If you know vectors
vector CB = (-2,3)
vector BA = (-3,-1)

v(CB) ∙ v(BA) = |CB||BA)cosØ, where Ø is our angle
6 - 3 = √13 √10 cos‚
cosØ = 3/√130 = .26311..
Ø = 74.74° as above.

Similar Questions

1. Geometry

Angle ABC and ange DBE are vertical angles,the measure of angle ABC =3x+20, and the measure or angle DBE =4x-10. Write and solve an equation to find the measure of angle ABC and the measure of angle DBEin
2. Geometry

Angle ABC and ange DBE are vertical angles,the measure of angle ABC =3x+20, and the measure or angle DBE =4x-10. Write and solve an equation to find the measure of angle ABC and the measure of angle DBEin
3. Math

Given the points A(0,0),B(3,1),and C(1,4), what is the measure of angle ABC?
4. Math

Given the points A(0,0)B(3,1), and C(1,4), what is the measure of angle ABC?
5. Geometry

ABC is an acute angle triangle with points D and E on BC and AC, respectively such that BE and AD are altitudes. AD and BE intersect at H. If \angle BCA = 39 ^\circ and \angle EBA = 2 \angle DAB , what is the measure of \angle ABC …
6. Geometry

ABC is an acute angle triangle with points D and E on BC and AC, respectively such that BE and AD are altitudes. AD and BE intersect at H. If \angle BCA = 39 ^\circ and \angle EBA = 2 \angle DAB , what is the measure of \angle ABC(in …
7. help math

In triangle ABC, points D,E,F are on sides BC,CA,AB respectively such that AD,BE,CF are angle bisectors of triangle ABC. The linesAD,BE,CF are concurrent at I,the incenter of triangle ABC. If Angle BAC=90, what is the measure (in degrees) …
8. Math

Given the points A(0,0), B(4, 3) and C(2,9), what is the measure of angle ABC?
9. Math

cosine law Given the points A(0,0) B (3,1) and C (1,4) what is the measure of angle ABC
10. Math

Given the points (A) 0,0 (B) 4,3 (C) 2,9 what is the measure of angle ABC

More Similar Questions