SOLUTION: What is the distance between the tips of the minute hand and the hour hand of a clock at 1:35pm where the length of the minute hand is 14cm and the length of the hour hand is 9cm

Question 1207171: What is the distance between the tips of the minute hand and the hour hand of a clock at 1:35pm where the length of the minute hand is 14cm and the length of the hour hand is 9cm
Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.
What is the distance between the tips of the minute hand and the hour hand
of a clock at 1:35pm where the length of the minute hand is 14cm
and the length of the hour hand is 9cm
~~~~~~~~~~~~~~~~~~~

At 1:35 pm, the angle between the minute hand and vertical direction up is  

     =  =   radians

(since the minute hand makes a full rotation in 60 minutes).


The angle between the hour hand and vertical direction up is

      +  =  +  = .

(since the hour hand makes a full rotation in 12 hours = 12*60 minutes).


The difference between these angles is

     -  =  -  = .


Thus the angle between the two hands at 1:35 pm is    radians.

It is more than the right angle  = , but less than the straight angle of  = .



Now, we have an obtuse triangle with the sides of 14 cm and 9 cm and the angle of   radians between them.


To find the distance between the tips of the hands, apply the cosine law equation

    d =  = 22.745 cm.


ANSWER.  The distance between the tips is about  22.745 cm.

Solved.

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