Posted by Rose on Tuesday, March 18, 2014 at 5:02am.
a clock has a dial face of 12 inches radius the minute hand is 9 inches while the hour hand is 6 inches the plane of rotation of the hour hand is 2 inches above the plane of rotation of the minute hand. Find the distance between the tips of the minute and hour hand at 5:40 am.

trigonometry  Steve, Tuesday, March 18, 2014 at 6:24am
let the plane of rotation of the minute hand be z=0. So, the location of the tip of the minute hand is
(9cosθ,9sinθ,0)
Similarly, the location of the tip of the hour hand is
(6cos θ/12,6sin θ/12,2)
at 5:40 am, θ = 2π/3, so θ/12 = π/18
So, the distance between the tips is
d^2 = (9cos 2π/3  6cos π/18)^2
+ (9sin 2π/3  6sin π/18)^2
+ 4
now just evaluate for d

trigonometry  Steve, Tuesday, March 18, 2014 at 6:27am
oops. Forgot all those hours
θ = 2π*5 + 2π/3 = 10π + 2π/3 = 32π/3
For the minute hand, that's the same value as 2π/3
but, θ/12 is now 32π/36 = 8π/9
which affects its trig function values immensely.
Answer This Question
Related Questions
 Geometry (math)  The 100foot clock tower in Rome, Georgia is more than 100 ...
 pre calc  the hour hand of a clock is 5 inches long and the minute hand is 6 ...
 PreClac  The height in inches about the ground of the tip of the hour hand is a...
 pre calculus  The minute hand and the hour hand of a clock have lengths inches ...
 trigonometry  The minute hand of a clock is 8 inches long. How far does the tip...
 calculus  A certain clock has a minute hand that is 4 inches long and an hour ...
 calculus  A certain clock has a minute hand that is 4 inches long and an hour ...
 Calculus  On a certain clock the minute hand is 4 inches long and the hour hand...
 math  the hour hand of a clock is 5 inches long and the minute hand is 6 inches...
 math  If the hour hand of a clock is 7 inches long, how many inches does the ...
More Related Questions