The number of degrees in an angle of a triangle is to the number of grades in the second is to the number of radians in the third as 288:280:pi. Find all the angles in degrees.

Question

It is a question about measurement of angles that includes sexagesimal system, centisimal system and circular measure.

Answer 1

The number of degrees in an angle of a triangle is to the number of grads in the second is to the number of radians in the third as 288:280:pi. Find all the angles in degrees.

We have the following definitions,

 

360 degrees = 2.pi radians

400 grads = 2.pi radians

400 grads = 360 degrees

 

So pi rad = 180 degrees

And 280 grads = (280/400)*360 = 252 degrees

So, the three angles are: 288, 252, 180 degrees

 

OK, I undersdtand your point. I originally thought there must be 3 separate triangles.

I have the three angles as 288, 252 and 180, which are in the ratios given.

As you said, the sum of the angles in a triangle add up to 180.

These three angles I got add up to 288 + 252 + 180 = 540 + 180 = 720

And 720 is 4 times 180. So just divide all the three angles by 4, to give

72, 63, 45, which are all in the proper ratio and add up to 180 degreres.

 

Sorry about the mixup.

Comments

It is not the required answer. You can just sum up all the degrees that you got the answer will be greater than 180 (sum of interior angles of a triangle is always 180 degrees). So.