Question

What is the acute angle between the hands of a clock when it is exactly 10 p.m.? (A) 30° (B) 45° (C) 60° (D) 75°

Short answer

The acute angle between the hands of a clock when it is exactly 10 PM is \(60°\) (option C).

Step-by-step solution

Calculating the position of the hour hand at 10 PM

At 10 PM, the hour hand will be exactly at 10. So its position is \(10 \times 30° = 300°\). Here, 30° is the angle covered by the hour hand in 1 hour (360°/12 hours).

Calculating the position of the minute hand at 10 PM

At the start of the 10th hour, the minute hand will be exactly at 12. So its position is \(0°\).

Calculating the acute angle between the hands of the clock

The acute angle between the two hands will be \(|(10 \times 30°) - (0 \times 6°)| = 300 °\). But that's the obtuse angle. The acute angle then is \(360° - 300° = 60°\). Therefore, the acute angle between the hands of a clock when it is exactly 10 PM is 60 degrees, so the correct answer is (C) 60°.

Key concepts

GED Practice Questions

Preparing for the General Educational Development (GED) tests can be challenging, but engaging with practice questions is a great way to enhance understanding and confidence. One common type of question found on the GED Mathematics test involves understanding the concept of angles and time, as exemplified by the clock angle problem.

When tackling GED practice questions, it's important to approach the problem methodically, just as you would in the provided clock angle example. First, you interpret the given problem to determine what you're being asked to find—in this case, the acute angle between the clock hands at a specific time. Next, breaking down the problem into manageable steps provides a clear pathway to the solution. Practice questions not only test your knowledge but also improve your problem-solving strategy, critical thinking, and your ability to apply mathematical concepts to real-world scenarios.

Acute Angle Calculation

An acute angle is one that is greater than 0 degrees but less than 90 degrees. Calculating an acute angle between the hands of a clock involves understanding the movement of the hour and minute hands. The clock is a circle, which has 360 degrees, and with 12 hours on the clock, each hour represents an angle of 30 degrees.

To determine the acute angle at a certain time, you calculate the angles from each hand to 12 o'clock and then find the difference between these two angles. Remember to always consider the smaller angle to find the acute angle. This concept is regularly used in various real-world applications beyond clocks, such as in geometry, architecture, and design; hence, mastering acute angle calculation is useful and quite essential.

Time Measurement Mathematics

Time measurement is an everyday concept that involves mathematics more than we usually appreciate. When we look at a clock, we are indirectly working with angles and divisions of a circle, as every minute and hour on the clock represents a certain degree of turn from a fixed point.

In time measurement mathematics, the position of the hour hand is dependent on the number of hours and the angle covered each hour (360 degrees divided by 12 hours). Meanwhile, the minute hand moves 360 degrees every 60 minutes, meaning it covers 6 degrees per minute (360 degrees divided by 60 minutes). Understanding these principles allows you to solve problems related to time and angles efficiently, fortifying your overall mathematical dexterity.