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Chapter 4: Problem 15

What is the angle between the hour hand and the minute hand on a clock at 4 o'clock?

Short Answer

Expert verified
The angle between the hour hand and the minute hand on a clock at 4 o'clock is 120掳.

Step by step solution

01

Determine the angle of the hour hand at 4 o'clock.

At 4 o'clock, the hour hand is 4/12 or 1/3 of the way around the clock. Because the clock is a circle of 360 degrees, this means that the hour hand is at an angle of \(\frac{1}{3} \times 360掳 = 120掳\) at 4 o'clock.
02

Determine the angle of the minute hand at 4 o'clock.

At 4 o'clock, the minute hand is at the 12 position, which means it is at an angle of 0 degrees.
03

Calculate the angle between the hour hand and the minute hand.

To find the angle between the hour and minute hands, subtract the angle of the minute hand (0掳) from the angle of the hour hand (120掳): \(120掳 - 0掳 = 120掳\) Therefore, the angle between the hour hand and the minute hand on a clock at 4 o'clock is 120掳.

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Most popular questions from this chapter

Explain why \(\sin 3^{\circ}+\sin 357^{\circ}=0\).

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Suppose \(u\) and \(v\) are in the interval \(\left(\frac{\pi}{2}, \pi\right),\) with $$\tan u=-2 \text { and } \tan v=-3$$ Find exact expressions for the indicated quantities. \(\cos v\)
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