Find clock time, given lines of hands

Question

I have a clock, and two hands for minutes and hours.

• Clock is centered somewhere around (165, -163)

I have two lines, represented by two points each. To be specific:

• (51, -143) and (173, -158) for the minutes hand.

• (198, -91) and (159, -165) for the hours hand.

The image looks like this: https://i.stack.imgur.com/vZuWi.png

Now, I need to calculate the time given this information. How should I go about it?

Small note: I am using matlab, and y-coordinates are actually written positively.

Answer 1

HINT:

Here is how much the hour hand travels per hour, minute, second:

• Per Hour: $$\text{H}=\frac{360^{\circ}}{12\space\text{hours}}=30^{\circ}\text{/}\space\text{hour}$$
• Per Minute: $$\text{M}=\frac{\text{H}^{\circ}}{60\space\text{minutes}}=\left(\frac{1}{2}\right)^{\circ}\text{/}\space\text{minute}$$
• Per Second: $$\text{S}=\frac{\text{M}^{\circ}}{60\space\text{seconds}}=\left(\frac{1}{120}\right)^{\circ}\text{/}\space\text{second}$$