Question

The vertices of a triangle are A(7, 5), B(4, 2), and C(9, 2). What is m`/_ABC`?

Answer 1

The measure of the angle is 45°

Explanation:

Correct on Plato

Answer 2

The vertices of a triangle are A(7, 5), B(4, 2), and C(9, 2)

First we need to find the length of each side of the triangle using Distance formula, d =
`image`

Length of side AB, c=
`√((7-4)^2 + (5-2)^2)`

=
`√((3)^2 + (3)^2)`

=
`√(9+9)`

=
`√(18)`

Length of side BC, a=
`√((4-9)^2 +(2-2)^2)`

=
`√((-5)^2 + 0)`

=
`√(25)`

= 5

Length of the side AC, b =
`√((7-9)^2 +(5-2)^2)`

=
`√((-2)^2 + (3)^2)`

=
`√(4+ 9) = <strong>√(13)</strong>`

Cos B =
`(a^2 + c^2 -b^2)/(2ac)`

Cos B =
`((5)^2 + (√(18))^2 - (√(13))^2)/(2*5*√(18))`

Cos B =
`(25+18-13)/(10√(18))`

Cos B=
`(30)/(10√(18))`

Cos B =
`(3)/(√(18)) = (3)/(3√(2)) = (1)/(√(2))`

By taking Inverse Cosine function,

B= Cos⁻¹ (
`(1)/(√(2))`)

B= 45°

The measure of angle ABC is 45°