What is the measurement of ∠C
if the image is rotated 305°
clockwise?
A=(2,5) b=(5,2) c=(2,2)
To find the measurement of ∠C after a rotation of 305° clockwise, we need to determine the original location of point C after the rotation.
First, let's plot the given points A, B, and C on a coordinate plane.
A = (2, 5)
B = (5, 2)
C = (2, 2)
Now, using the given rotation of 305° clockwise, we can determine the new coordinates of point C.
To rotate a point (x, y) clockwise by an angle θ, the new coordinates (x', y') can be found using the following formulas:
x' = x * cos(θ) + y * sin(θ)
y' = -x * sin(θ) + y * cos(θ)
Applying this formula with θ = 305° and (x, y) = (2, 2):
x' = 2 * cos(305°) + 2 * sin(305°)
y' = -2 * sin(305°) + 2 * cos(305°)
Using a calculator to evaluate these trigonometric functions, we find:
x' ≈ -0.524
y' ≈ 3.831
Therefore, the new coordinates of point C after the rotation are approximately (-0.524, 3.831).
Now we can simply find the angle ∠C by using the appropriate trigonometric function. However, without knowing the positions of any other points, it is not possible to find the exact measurement of ∠C.