Answered

Find the measure of the smaller angle formed by hands of a clock at the following time.


5:15

Verified Answer :

wizard123

A clock is a circle which is 360 degrees.

There are 12 hours -----> 360/12 = 30 degrees.

Going clockwise, add 30 degrees for every hour the hour hand is at.

There are 60 minutes -----> 360/60 = 6 degrees.

Add 6 degrees for every minute the minute hand is at.

Find position of both hour hand and minute hand, then take the difference.

Time is 5:15.
Hour hand is at 5 plus 15/60 or 5.25.
Multiply by 30. 305.25 = 157.5

Minute hand is at 15.
Multiply by 6. 156 = 90

157.5 - 90 = 67.5 degrees.

The measure of the smaller angle formed by the hands of a clock at the following time of 5:15 is; 67.5°

Clock Hands Angle

A clock is basically a circle with a total angle of 360°.

In a clock, there are 12 total hours and so;

Degree per hour =  360/12 = 30°

For every one hour the angle 30° will be added (both hands).

Now, as the same 15 minutes as 1/4 hour (for the hour hand) will yield = (30/4) = 7.5°

Therefore at the time of 5.15 hours, the hands angle is;

(30 * 5) + 7.5 =  157.5°

For the minute hand, we know that 15 minutes angle is 90°.

Thus;

Angle between both hands = hour hands angle - minute hands angle

Angle between both hands = 157.5° - 90° = 67.5°

Read more about the clock hands angle at; https://brainly.com/question/1612098

Related Questions