Question

Use vectors to find the interior angles of the triangle with the given vertices.

(1, 2),  (3, 4),  (2, 5)

Answer 1

Step 1:

The vertices of triangle are , and .

Let  , and .

Angle between two vectors : .

Find angle between AB and AC.

The vector from to is .

The vector from to is .

Magnitude of AB is .

Magnitude of AC is .

Dot product of AB and AC is

Angle

Answer 2

Contd..

Step 2:

Find angle  between AB and BC.

The vector from to is .

The vector from to is .

Magnitude of AB is .

Magnitude of BC is .

Dot product of AB and BC is .

Angle

Step 3:

Properties of triangle : Sum of all angles in a triangle is

Solutions:

Interior angle of triangle are , and .