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 100-foot 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