Acute and obtuse
"When the Angles (with the Saxons) invaded England, they settled in what became known as the Land Debatable, namely the north of England and the south of Scotland. The acute Angles went north and the obtuse ones south."
Consider a triangle. Let be the maximum possible number of acute angles it can have.
Now consider a second triangle. Let be the maximum possible number of obtuse angles it can have.
Find
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
By the definition of "triangle", it has three angles in it. Those angles must add up to 180 degrees.
Definition of an acute angle: one that is less than 90 degrees. We can accommodate 3 of those in a triangle: for example: a triangle with angles of 45, 60 and 75 degrees. So A = 3
Definition of an obtuse angle: one that is more than 90 degrees. If we accommodate one of those, subtracting from 180 means the other two angles combined must be less than 90. (For example: 130 degrees, 30 degrees, 20 degrees.) So O = 1
3 − 1 = 2