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What is the degree measure of the smaller angle formed by the minute hand and the hour hand of a clock at 3:30?

 Jun 21, 2018

Ahh, the clock problem!


First, the minute hand crossed 180 degrees(half the clock), and the hour hand crossed 90 degrees and a small portion between 3 and 4.


We know also know that 30 degrees of the hour hand, equals 360 degrees of the minute hand.


Equating our formula, we have \(30^\circ=360^\circ\)


Then, finding the hour hand, by plugging in 180 degrees for the minute hand, we get: \(\frac{30^\circ}{2}=15^\circ\).


The question is asking us to find the distance of the smaller angle. Note that this is not referring to the small hand.


At 3:30, the smaller angle would be: \(60^\circ+15^\circ=\boxed{75^\circ}\) .


 Jun 21, 2018

You can also use this formula:


A =1/2 x abs[(60 x H) - (11 x M)]
A =Angle
H =Hour

Angle = 1/2 x abs[(60 x 3) - (11 x 30)]

Angle = 1/2 x abs[180 - 330]

Angle = 1/2 x abs[ -150 ]

Angle = 1/2 x 150

Angle = 75 degrees.

Note : If the angle is > 180 degrees, then you subtract it from 360 degrees.

 Jun 21, 2018

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