A (4,3)
B (3,-3)
c (-4,5)
Find the slope of AB, BC, and AC. Fond the tangent of each angle and their angle measure
using: tanX=m2-m1/1+m1m2
m2 being the slope of the terminal side (measuring counterclockwise)
To find the slopes of the line segments AB, BC, and AC, we can use the formula:
slope = (change in y)/(change in x)
Let's calculate the slopes of these line segments one by one:
1. Slope of AB:
The coordinates of point A are (4,3), and the coordinates of point B are (3,-3).
The change in y is: -3 - 3 = -6
The change in x is: 3 - 4 = -1
So, the slope of AB is: (-6)/(-1) = 6
2. Slope of BC:
The coordinates of point B are (3,-3), and the coordinates of point C are (-4,5).
The change in y is: 5 - (-3) = 8
The change in x is: -4 - 3 = -7
So, the slope of BC is: 8/(-7)
3. Slope of AC:
The coordinates of point A are (4,3), and the coordinates of point C are (-4,5).
The change in y is: 5 - 3 = 2
The change in x is: -4 - 4 = -8
So, the slope of AC is: 2/(-8) = -1/4
Now, let's find the tangent of each angle using the formula:
tanX = (m2 - m1) / (1 + m1 * m2)
For angle ABC:
m1 = slope of AB
m2 = slope of BC
tan(ABC) = (m2 - m1) / (1 + m1 * m2)
For angle BCA:
m1 = slope of BC
m2 = slope of AC
tan(BCA) = (m2 - m1) / (1 + m1 * m2)
For angle CAB:
m1 = slope of AC
m2 = slope of AB
tan(CAB) = (m2 - m1) / (1 + m1 * m2)
We can substitute the values we calculated earlier to find the tangents of each angle and their angle measures.