Answer
a) 2.48 cm, 18.4°
b) 4.09 cm, 83.7°
c) 4.09 cm , 264°
Work Step by Step
a)
A= 2.80 cm
Ax = Acos(60) = 2.80 x cos(60) = 1.4 cm
Ay= Asin(60) = 2.80 x sin(60) = 2.428 cm
B= 1.90cm
Bx= Bcos(60) = 1.90 x cos(60) = 0.95 cm
By= Bsin(60) = 1.90 x sin(60) = -1.645 cm
C= A + B
Cx = Ax + Bx = 1.4 + 0.95 = 2.35 cm
Cy= Ay + By = 2.428 - 1.645 = 0.783 cm
C= ((Cx)^2 + (Cy)^2))^1/2
C= 2.4778 = 2.48 cm
\theta = Tan^-1 (0.783/2.35) = 18.4°
b)
Ax= 1.4 cm ; Ay= 2.428 cm
Bx= 0.95 cm ; By= -1.645 cm
C = A - B
Cx = Ax- Bx = 1.4 - 0.95 = 0.45 cm
Cy = Ay - By = 2.428 + 1.645 = 4.073 cm
C = ((0.45)^2 + (4.073)^2)^1/2
C= 4.09 cm
\theta= Tan^-1(4.073/0.45) = 83.69° = 83.7°
c)
Ax= 1.4 cm ; Bx= 2.428 cm
Ay= 0.95 cm ; By= - 1.645 cm
C= B - A
Cx = Bx - Ax = 0.95 - 1.4 = - 0.45 cm
Cy = By - Bx = -1.645 - 2.428 = -4.073 cm
C= ((-0.45)^2 + (-4.073)^2)^1/2 = 4.09 cm
\theta = Tan^-1( -4.073/-0.45) = 83.7 °
180° + 83.7° = 263.7° = 264°
