Final answer:
To solve a problem involving angle measurements, such as determining the angle moved by a clock's minute hand in 15 minutes, divide the full rotation (360 degrees or 2π radians) by the proportion of time passed and convert to radians if necessary, then check for reasonableness.
Step-by-step explanation:
To tackle a real-world problem involving angle measurements, consider the situation of a clock tower. Assume you want to calculate the angle through which the minute hand moves in 15 minutes. Start by identifying the known values: the minute hand completes a full rotation (360°) in 60 minutes. Therefore, in 15 minutes, it would cover a quarter of the rotation. To solve this, you divide 360° by 4, which gives 90° or, converting into radians, π/2 radians.
Next, substitute the known values into the appropriate equation for angular rotation (θ = ω × time), where θ is the angle in radians, and ω is the angular velocity. Since we already have θ (90° or π/2 radians), we can verify that it's indeed a quarter of 360° and therefore reasonable for 15 minutes of movement of the minute hand.
For problems involving larger complexities, such as constructing non-standard geometric shapes or measuring the angular speed of an object, always ensure to convert angles into radians and check that the obtained values make sense within the context of the problem.