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.