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

hatchet288  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: \(60^\circ+15^\circ=\boxed{75^\circ}\) .


tertre  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.

Guest Jun 21, 2018

15 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.