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

#1**+3 **

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

#2**+2 **

You can also use this formula:

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

A =Angle

H =Hour

M=minute

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