trig homework help

Question

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 five o'clock. Round your answer to the nearest hundredth of an inch.

Answer 1

hour hand 4.5 inches

minute hand 6 inches

at 5:00 o'clock

the distance between the ends of the two hands is: about 10.15 inches

helps to sketch a diagram of the clock

5 is 5/6 of the way from 12 to 6, 5/6 of 180 degrees = 150 degrees

minute hand is pointing to the 12, hour hand to the 5

150 degrees between them

This is an SAS problem

use the law of cosines

d^2 = 4.5^2 + 6^2 -2(4.5)(6)Cos150

= 20.25 +36 - 54(-sqr3/2)

= 56.25 +27sqr3

= about 56.25 +27(1.732)

= about 103.0153718

d=sqr(103.0153718)

= about 10.1496

= about 10.15 inches

at 6:00 o'clock

d= 6+4.5= 10.5

at 5:00 o'clock it's slightly less