# Height of minute hands off a clock

• Oct 1st 2009, 03:12 PM
algebraisabeast
Height of minute hands off a clock
A large clock with rotating hour and minute hands is on a building with its center 20 feet tall. The length of the hour hand is 1.5 feet in length and the length of the minute hand is 2 feet. At 8:20, give the height off the ground of the tip of each hand

20+2sin(330)= 19 feet of the ground for the minute hand

20+1.5sin(-160) How do we find the degree of rotation for this problem?
• Oct 1st 2009, 04:19 PM
skeeter
Quote:

Originally Posted by algebraisabeast
A large clock with rotating hour and minute hands is on a building with its center 20 feet tall. The length of the hour hand is 1.5 feet in length and the length of the minute hand is 2 feet. At 8:20, give the height off the ground of the tip of each hand

20+2sin(330)= 19 feet of the ground for the minute hand

20+1.5sin(-160) How do we find the degree of rotation for this problem?

you already have it ...

8 hrs 20 min = 8 and 1/3 hrs

after 8 and 1/3 hrs, the hour hand rotates [8 + (1/3)]/12 * 360 degrees = 250 degrees clockwise from the 12 o'clock position.

relative to the +x-axis, that angle is coterminal with -160 degrees

$y = 20 + 1.5\sin(-160^\circ)$