Find the angle between the line y=2x and the line passing through the points(-1;7/3 ) and (0;2)
Y = 2x
Tan A = m1 = 2
A = 63.43o
(-1,7/3),(0,2).
m2 = Tan B = (2-7/3)/(0+1) = (-1/3)/1 =
-1/3.
B = -18.43o = -18.43o
C = A-B = 63.43 - (-18.43) = 81.9o =
Angle between A and B.
To find the angle between two lines, we need to find the slopes of the lines first.
The line y = 2x is in the form y = mx + c, where m is the slope. In this case, the slope is 2.
The line passing through the points (-1, 7/3) and (0, 2) can be found by using the formula: slope (m) = (y2 - y1) / (x2 - x1).
Substituting the coordinates into the formula:
m = (2 - 7/3) / (0 - (-1))
= (2 - 7/3) / (0 + 1)
= (6/3 - 7/3) / 1
= (-1/3) / 1
= -1/3
Now the slope of the second line is -1/3.
To find the angle between the two lines, we can use the formula: angle = arctan(|(m1 - m2) / (1 + m1 * m2)|)
Substituting the slopes into the formula:
angle = arctan (|(2 - (-1/3)) / (1 + 2 * (-1/3))|)
= arctan (|(2 + 1/3) / (1 - 2/3)|)
= arctan (|(6/3 + 1/3) / (3/3 - 2/3)|)
= arctan (|(7/3) / (1/3)|)
Now, we can calculate the value of arctan(7/3) / (1/3) using a calculator or math software, this value will give us the angle between the two lines.