We've been learning about angles. My class wants to know why a right angle has 90 degrees?

submitted by the students from Ms. Pham's class
Morris Avenue Intermediate School, Opelika

Dear students in Ms. Pham's class,

There are really two things to look at in the question - where does the "90" come from and why is it called a "right" angle. The first has a historical answer, the second a linguistic one. Our custom of using a 90 degree angle for a right angle comes from the ancient Babylonian civilization. They were great star gazers and astronomers. As part of their study of astronomy they needed a way to measure the "elevation" of the different stars and planets: if you look at the different stars at night you'll bend your neck different amounts depending on how "high" a star seems to be. A measure of the amount that you bend your neck says something about this quantity. Since the earth moves, a star's elevation will change at different times of the day. A way of measuring this is to say something like, "that star is halfway up now" or "at sunset Mars is three-fifths of the way up."

But the Babylonians felt that using fractions could be complicated so they divided a circle into 360 equal "degrees." The reason they picked 360 also comes from their number system. Their number system was based on the number 60 and 360 is 6 times 60. The thing that's special about 360 is that you can express a lot of fractional parts of 360 degrees with whole numbers of degrees. The fractions 1/2, 1/3, 1/4, 1/5 and 1/6 of 360 all come out as whole numbers. The fraction 1/7 doesn't but the fractions 1/8, 1/9 and 1/10 also come out as whole number of degrees from 360. So the only number from 1 to 10 that was missed as an even fraction was 7 and I guess they felt this was pretty good. So that's where the 360 comes from. Looking straight up at the night sky is one quarter of the way around the circle (move your arm in a circle and as it moves from straight out to straight up, it goes one quarter of the way around); one quarter of 360 degrees is 90 degrees. (See, no fraction! The star that was half way up would be half way up from 90 degrees so it would be at 45 degrees; the position of Mars mentioned would then be at 54 degrees elevation.)

The word "right" is used for this angle because the word has the meaning of "true" or "correct." When a carpenter is building a house and he positions a wall, he wants that wall to be correctly placed; to be "right" or "true." So when the wall is vertical then it is correctly placed or "true." A correctly placed "true" wall is perfectly vertical and so it makes a "right" angle with the ground. This is what a right angle or a 90 degree angle is.

Thanks for your question,
Aubie and Dr. Smith