A (4,3)
B (3,-3)
c (-4,5)
Find the slope of AB, BC, and AC. Find the tangent of each angle and their angle measure (inv. tan)
using: tan of an angle =m2-m1/1+m1m2
m2 being the slope of the terminal side (measuring counterclockwise)
the triangle looks like this
c
a
b
To find the slopes of the line segments AB, BC, and AC, we can use the formula for slope:
Slope (m) = (y2 - y1) / (x2 - x1)
Let's calculate the slope of AB:
Point A: (4, 3)
Point B: (3, -3)
Slope (AB) = (-3 - 3) / (3 - 4) = -6 / -1 = 6
So, the slope of AB is 6.
Next, let's calculate the slope of BC:
Point B: (3, -3)
Point C: (-4, 5)
Slope (BC) = (5 - (-3)) / (-4 - 3) = 8 / (-7) = -8/7
So, the slope of BC is -8/7.
Lastly, let's calculate the slope of AC:
Point A: (4, 3)
Point C: (-4, 5)
Slope (AC) = (5 - 3) / (-4 - 4) = 2 / (-8) = -1/4
So, the slope of AC is -1/4.
Now, let's find the tangent of each angle:
To find the tangent of an angle, we can use the formula:
Tangent of an angle = (m2 - m1) / (1 + m1 * m2)
Let's calculate the tangent of angle BAC:
Tangent (BAC) = (6 - (-1/4)) / (1 + (6 * (-1/4))) = (25/4) / (1 - 3/4) = (25/4) / (1/4) = 25
The tangent of angle BAC is 25.
Next, let's calculate the tangent of angle ABC:
Tangent (ABC) = ((-8/7) - 6) / (1 + (6 * (-8/7))) = (-50/7) / (1 - (48/7)) = (-50/7) / (-41/7) = 50/41
The tangent of angle ABC is 50/41.
Lastly, let's calculate the tangent of angle BCA:
Tangent (BCA) = ((-1/4) - (-8/7)) / (1 + ((-8/7) * (-1/4))) = (37/28) / (1 + (2/7)) = (37/28) / (9/7) = 37/36
The tangent of angle BCA is 37/36.
Please note that to find the angle measure from the tangent value, you would use the "inverse tangent" function (usually denoted as "tan⁻¹" or "atan") on a calculator or software. For example, to find the angle measure of BAC from the tangent value of 25, you would use the inverse tangent function: angle BAC = tan⁻¹(25).