Answer:
(5, 8.66)
Step-by-step explanation:
Let x represent the x coordinate of the clock tip and y represent the y coordinate of the clock tip.
At 12:05 pm, the clock tip forms an angle of 60° with the x axis. Therefore:
θ = 60°
[tex]tan\theta=\frac{y}{x} \\\\tan60=\frac{y}{x} \\\\y=1.732x\\\\y-1.732x=0\ \ \ (1)[/tex]
Since the minute hand is 10 inches long, hence:
[tex]\sqrt{x^2+y^2}=10\\\\x^2+y^2=100\\\\substituting\ y=1.732x, gives\\\\x^2+(1.732x) ^2=100\\\\x^2+3x^2=100\\\\4x^2=100\\\\x^2=25\\\\x=5[/tex]
To find y, substitute x = 5:
y = 1.732(5) = 8.66
This means that the coordinate of the tip of the minute hand at: 12:05 p.M. is (5, 8.66)
