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

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

its line 2 i just added the rest or else it wouldn't let me answer