Question

1. Is a triangle with sides of 20, 30, and 11 acute, obtuse, right, or not a triangle.

Answer 1

obtuse

Explanation:

Given the 3 sides 20, 30 and 11

For the sides to form a triangle then the sum of any 2 sides must be greater than the third side.

20 + 30 = 50 > 11

20 + 11 = 31 > 30

30 + 11 = 41 > 20

Thus the 3 sides form a triangle

To determine what type of triangle it is

let c be the longest side and a, b the other 2 sides

• If a² + b² = c² then triangle is right

• If a² + b² > c² then triangle is acute

• If a² + b² < c² then triangle is obtuse

Here c = 30, a = 20, b = 11

c² = 30² = 900

a² + b² = 20² + 11² = 400 + 121 = 521

Since a² + b² < c² then triangle is obtuse

Answer 2

as 20+11>30 it is a triangle

now for angle

let us consider a=20,b=30,c=11 and their opposite angle be A,B,C respectively

then B =cos-inverse((a^2 +c^2-b^2)/2ac))

p.s We are calculating value of B because it is opposite of largest side b so it will be highest angle

or B = cos-inverse((400+121-900)/(2*30*11))

B = 125.04 degree

since B> 90 the triangle is obtuse triangle