Question

Triangle AABC is rotated -120° about point P to create triangle AA'B'C'.

A) 105°

B) 140°

C) 175°

D) 120°

Answer 1

The question involves finding the sum of two vectors given in polar form. By converting them into rectangular components and then combining these components, we can determine the magnitude and direction of the resultant vector.

Step-by-step explanation:

The question pertains to the rotation of a triangle in the plane and appears to include a typing error. Given the context of vector addition and geometric transformation, the relevant question extracted seems to involve calculating the sum of vectors A and B, where:

• Vector A = (122 cm, < 145°)
• Vector B = (110 cm, < 270°)

To find the resultant vector, we break down both vectors into their components:

• Ax = 122 cm × cos(145°)
• Ay = 122 cm × sin(145°)
• Bx = 110 cm × cos(270°) = 0 (since cos(270°) = 0)
• By = 110 cm × sin(270°) = -110 cm (since sin(270°) = -1)

Now we sum the x and y components of vectors A and B to find the resultant vector R:

• Rx = Ax + Bx
• Ry = Ay + By

The magnitude of vector R is obtained by the square root of (Rx² + Ry²), and the angle can be calculated using the inverse tangent of Ry/Rx.