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What is the number of degrees in the measure of the smaller obtuse angle formed by the hands of a standard clock at 2:48pm?

(i think it might be 156 degrees but I'm not sure)

 Mar 26, 2020
edited by amphat100  Mar 26, 2020
 #1
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To understand the question better, it's easier to actually get an image, so I used : https://www.visnos.com/demos/clock

 

Lets solve for the hour. 

 

12 hours = 360°

1 hour or 60 mins = 30°

 

You would count all hours within the minute and hour hands. There are 5 hours in between. So because 1 hour is equal to 30°, you would multiply 5 and 30, which would then be 150°.

 

Let's solve for the minute.

 

This is where the image is good to have. It wants the obtuse angle, so you would subtract 60 from 48, which would leave you with 12 minutes left. Because 60 minutes is equal to 30°, you would then cross multiply with something that looked like this:

60  /  30      =      12  /  x

 

Solve for x and you would get 6°

 

Add your degrees 150° and 6°. Your answer is 156°. Voila! laugh

 Mar 26, 2020
 #2
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Thank you!

 Mar 26, 2020
 #3
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H=2; M=48; A=abs((30*H) - (5.5*M));print"A =", A,"Degrees")

 

A = 204 Degrees

The minute hand is at 48 minutes. That is clear. The hour hand has moved: 48 / 12 = 4  minutes after 2, which is 14 minutes from 12 O'clock. So, 48 - 14 =34 minutes, the angle between the two hands of the clock. But each minute on the clock is 360 /60 =6 degrees . Therefore, 34 minutes x 6 degrees =204 degrees.

 Mar 26, 2020
 #4
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What you calculated is true, but that is the larger obtuse angle. He/She wants the smaller obtuse angle. So, 360 - 204 = 156 degrees.

Guest Mar 26, 2020

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