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.

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.

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

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

Can you simplify?