Okay, heres the problem
The hands of a round faced clock have lenghts 10cm and 7cm. Calculate the distance between the tips of the hands at 8:00.
How do you find the missing angle to solve the problem?
2007-04-07 11:14:34 · 3 answers · asked by Thinker 3 in Science & Mathematics ➔ Mathematics
From 8 to 12 on the clock is 20 min, or 1/3 hour, 1/3 of the circle, 120°.
After that, d² = 10² + 7² - 2(7)(10)cos 120 = 149 - 140(-1/2) = 149 + 70 = 219
d = √219 = 14.8 cm.
2007-04-07 11:21:07 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
there are four hours between 8 and 12, so 4/12 (1/3) of the full circle, or 120 degrees (2pi/3 in radians). That's the angle between the two hands.
2007-04-07 18:21:35 · answer #2 · answered by bz2hcy 3 · 0⤊ 0⤋
Each hour is 1/12 of a complete revolution of 360deg. Therefore each hour corresponds to 30deg. and so between 8 and 12 you have 120deg.
2007-04-07 18:22:05 · answer #3 · answered by mathsmanretired 7 · 0⤊ 0⤋