How many acute angles can a scalene triangle have?

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Answer 1 · 2015-11-23T03:30:42

A scalene triangle can have either $2$ or $3$ acute angles.

A scalene triangle is any triangle with no repeated angle measures.

There are three general ones:

An acute scalene triangle, where all $3$ of the angles are less than $90˚$ . An example would be a triangle with degree measures $30˚$ , $70˚$ , and $80˚$ . All three of its angles have different measures and are all acute. (3 acute angles)
A right scalene triangle. Any right triangle will have one degree whose measure is $90˚$ , and the other two angles must be acute. An example would be the very common $30˚-60˚-90˚$ triangle, which, again, has two acute angles. (2 acute angles)
An obtuse scalene triangle. This is very similar to the right scalene triangle, except it has one angle whose measure is greater than $90˚$ , and two acute angles. (2 acute angles)