Question

Is the triangle with side lengths 20, 23, and 41 acute, right, obtuse, or not a triangle?

Answer 1

It's an Obtuse Angle Triangle .

Explanation:

1) If sum of the two smaller sides of a triangle is greater than the third longer side, then its a triangle.

In our case, 20 + 23 > 41. Hence its a triangle .

Use the side lengths to classify the triangle as acute, right, or obtuse. Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides

2) Square root of sum of the squares of the two smaller sides is equal to the third longer side, then its a right triangle.

In our case, `sqrt(20^2 + 23^2) ~~ 30.4795 < 41`. Hence not a right triangle.

Since the sum of the squares of the two shorter sides is < the square of the longer side, its an obtuse angle triange