The Clock Face

At 3 o'clock, the angle formed between the two hands is 90 degrees.

What is the angle formed by the hands at exactly 3:15?

The Solution

To solve this question, you’ll have to visualize the clock hands at 3:15.

At 3:15, the minute hand would be exactly at the 3-hour marker. Since a quarter of an hour has passed, the hour hand moves ¼ away from the 3-hour on its way to the 4-hour marker. There are 12 hour-markers on the clock-face, and each hour-marker must be 30 degrees (360 degrees divided by 12). And ¼ of 30 degrees is 7.5 degrees. So that’s the angle formed between the two hands at exactly 3:15.

Tip: Omerus lets you reuse any number from your previous calculations by simply tapping on it

How to solve with Omerus?

You can break this problem down, line by line using Omerus as shown below:

360 / 12 = 30

Degrees in a circle divided by 12 hours = 30 degrees in 1 hour

15 / 60 = 0.25

15 mins divided by 60 mins = 0.25 (the ratio the hour hand has moved from 3 towards 4)

30 x 0.25 = 7.5

Degrees in 1 hour x the amount the hand has moved = 7.5 degrees