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.

Question

contestada

Respuesta :

znk znk · Answer 1 · 2020-03-15T02:27:08+01:00

Answer:

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.

boffeemadrid boffeemadrid · Answer 2 · 2021-10-21T12:32:32+02:00

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.

[tex]\dfrac{360}{12}=30^{\circ}[/tex]

So, at 4 o'clock the angle will be

[tex]\theta=4\times 30=120^{\circ}[/tex]

[tex]a=6[/tex]

[tex]b=4.5[/tex]

From the law of cosines we get

[tex]c=\sqrt{a^2+b^2-2ab\cos\theta}\\\Rightarrow c=\sqrt{6^2+4.5^2-2\times 6\times 4.5\cos120}\\\Rightarrow c=\sqrt{83.25}=9.12[/tex]

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

Learn more:

https://brainly.com/question/17158306

https://brainly.com/question/14308706