The minute hand on a watch is 8 mm long and the hour hand is 7 mm long. How fast is the distance between the tips of the hands changing at one o'clock? (Round your answer to one decimal place.)

Question

Answer as best you can:)

Answer 1

at 1 o'clock the angle between the hands = 360/12= 30 degees

big hand on the 12, smaller hand on the 1. full circle is 360 degrees

12 to 1 is 1/12 of the circle = 360/12 = 30 degrees

it's as sas triangle: 8 - 30 -7

use law of cosines

c^2= 64+49-2(56)Cos30

= 113-112(sqr3/2)= 113 - 112(1.732)/2 = 113 -56(1.732)=about 113-96.995 = about 16.005

c = about sqr16.005 = 4.00062= about 4.0 mm

c^2 =a^2+b^2-2abCosC

take the derivative with respect to time

plug in the values, and solve for c'