Question

the ferris wheel stopped during its initial rotation when michael was at the point (-33.807, -9.059). a. what is the measure of the angle (in radians) that has a vertex (0,0) and rays through the point (35, 0) and (-33.807, -9.059)?

Answer 1

To find the measure of the angle in radians, use the formula for finding the angle between two vectors. Calculating this, we find that the angle is approximately 2.368 radians.

Step-by-step explanation:

To find the measure of the angle in radians, we can use the formula for finding the angle between two vectors:

cos(theta) = (a · b) / (|a| |b|)

where a and b are the vectors with components (35, 0) and (-33.807, -9.059) respectively.

Calculating the values and substituting them into the formula, we get:

cos(theta) = ((35)(-33.807) + (0)(-9.059)) / (√((35)^2 + 0^2) √((-33.807)^2 + (-9.059)^2))

Cosine inverse both sides to find theta:

theta = cos^+1(((35)(-33.807) + (0)(-9.059)) / (√((35)^2 + 0^2) √((-33.807)^2 + (-9.059)^2)))

Calculating this, we find that theta is approximately 2.368 radians.