# Give an expression

• Nov 1st 2008, 11:46 AM
gearshifter
Give an expression
The minute hand on a clock is 8 cm long and the hour hand is 5 cm long. Give an expression for d, the distance between the tips of the hands, in terms of a, the angle between the hands.

D=

I've been trying to figure this out for the past hour... needless to say, I just have problems with these questions.
• Nov 1st 2008, 05:41 PM
masters
Quote:

Originally Posted by gearshifter
The minute hand on a clock is 8 cm long and the hour hand is 5 cm long. Give an expression for d, the distance between the tips of the hands, in terms of a, the angle between the hands.

D=

I've been trying to figure this out for the past hour... needless to say, I just have problems with these questions.

It would seem that this is a classic application of the law of cosines.

You have an angle a included between two sides 8 and 5. The side opposite angle a, which is D is the distance between the the two hands.

$D^2=8^2+5^2-2(8)(5)\cos a$

$D=\sqrt{8^2+5^2-2(8)(5)\cos a}$

Can you simplify?