Question

The hour hand on my antique schoolhouse clock is 4 inches long and the minute hand is 5.8 inches long. Find the distance between the ends of the hands when the clock reads four o'clock.

Answer 1

r = 6.5 inch.

Explanation:

The given data :-

• The length of the hour hand = 4 inches.
• The height of the minute hand = 5.8 inches.

Solution:-

∵ Angle traced by hour hand in 12 hour = 360°

∴ Angle traced by hour hand in 4 hour =
`(360)/(12) *4` = 120°

The distance between the ends of the hand of the clock is given by ( r )

r² = (3.5)² +( 4)² - 2 x 3.5 x 4 cos ( 120⁰ ) = 12.25 + 16 + 14 = 42.25

r = 6.5 inch.