The hour hand on my antique Seth Thomas schoolhouse clock is 4.5 inches long and the minute hand is 6 long. Find the distance between the ends of the hands when the clock reads four o'clock. Round your answer to the nearest hundredth of an inch.

The distance between the hour and minute hand is required at 4 o'clock.

The distance between the minute hand and hour hand at 4 o'clock would be 9.12 inches.

Since, the clock is circular the angle between the hour and minute hand at 1 o'clock.

So, at 4 o'clock the angle will be

From the law of cosines we get

The distance between the minute hand and hour hand at 4 o'clock would be 9.12 inches.

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9.12 in  

Step-by-step explanation:

The distance between the two hands is the length of AB in ∆AOB below.

1. Calculate the angle θ between the hands.

The hour hand travels a full circle (360°) in 12 h. or 30°/h.

In 4 h, it has travelled 4 × 30°.

θ = 120°

2. Calculate the distance between the ends of the hands

We have a triangle with sides 6 in and 4½ in and an included angle of 120°.

We  can use the Law of Cosines to find side AB.

AB² = a² + b² - 2abcosθ = 4.5² + 6² - 2 × 4.5 × 6 × cos 120°

                                       = 20.25 + 36 - 54 × 0.5 = 56.25 + 27

                                       = 83.25

AB = √(83.25) = 9.12 in

The distance between the ends of the hands is 9.12 in.

c

step-by-step explanation:

f(x)=2/3x-8, which give g(x) the greatest value.

step-by-step explanation: