Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle.

Question

The vertices of a triangle are given. Determine whether the triangle is an acute triangle, an obtuse triangle, or a right triangle. Explain your reasoning.

Answer 1

Step 1:

The vertices of the triangle are and .

Consider the vectors , and are the sides of the triangle.

The component form of a vectors , and are

The magnitude of the vectors are

Step 2:

The angle between two vectors and is .

The angle between and .

.

The angle between and .

.

The sum of angles in a triangle is .

.

The triangle that has all the angles less than .

So, the triangle is acute triangle.

Solution:

The triangle is acute triangle.