Item 7 △ABC has vertices A(−1, 2), B(2, 8), and C(4, 1). Find the measure of each angle of the triangle. Round decimal answers to the nearest tenth.

Step-by-step explanation:

Given

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

For AB

So:

For BC

For AC

So, we have:

By representation

So, we have:

By cosine laws, the angles are calculated using:

Collect like terms

Solve for

Take arc cos of both sides

Collect like terms

Solve for

Take arc cos of both sides

For the third angle, we use:

--- angles in a triangle

Make C the subject

73.0769230769% of the games were won