Answer:
Obtuse
Step-by-step explanation:
a^2 + b^2 = c^2
10^2 + 11^2 = 16^2
100 + 121 = 256
221 = 256
221 < 256
A triangle has side lengths 10, 16, and 11. is the triangle is obtuse.
Triangles can be classified into three types with respect to their interior angles which are:
1. Acute-angled
2. Obtuse-angled
3. Right-angled
Acute Triangle
An acute triangle is a triangle whose all the three interior angles are acute. In other words, if all interior angles are less than 90 degrees, then it is an acute-angled triangle.
Obtuse Triangle
Obtuse triangles are those in which one of the three interior angles has a measure greater than 90 degrees. In other words, if one of the angles in a triangle is an obtuse angle, then the triangle is called an obtuse-angled triangle.
Right Triangle
A right triangle is a triangle in which one of the angles is 90 degrees. In a right-angled triangle, the side opposite to the right angle (90-degree angle) will be the longest side and is called the hypotenuse.
Three given sides are 10, 11, 16
Let a = 10, b = 11, c = 16
then, [tex]a^{2} +b^{2} = 10^{2} +11^{2}[/tex]
= 100 + 121
= 221
and [tex]c^{2} = 16^{2} =256[/tex]
Since, [tex]a^{2} +b^{2} < c^{2}[/tex]
Thus, given triangle is obtuse.
Find out more information about types of triangles here
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