In triangle ABC, a, b and c are opposite sides of A, B and C respectively, and a^3+b^3= c^3, ask whether the triangle is an acute triangle or an obtuse triangle In triangle ABC, a, b, c are opposite sides of A, B, and C, and a^3+b^3= c^3, ask whether the triangle is an acute triangle or an obtuse triangle

In triangle ABC, a, b and c are opposite sides of A, B and C respectively, and a^3+b^3= c^3, ask whether the triangle is an acute triangle or an obtuse triangle In triangle ABC, a, b, c are opposite sides of A, B, and C, and a^3+b^3= c^3, ask whether the triangle is an acute triangle or an obtuse triangle

A^3+b^3= c^3
And a, b, c >0
So c > a, and c > b, that is, c is the largest edge, so C is the largest angle
So c^2=a^3/c+b^3/c=a^2*a/c+b^2*b/c can be judged to be an acute triangle.
If it's not clear, according to the cosine theorem
C^2= a^2+b^2-2ab*cosC has cosC >0, that is, C is an acute angle, and because C is the maximum angle, ABC is an acute triangle.

The three sides of the triangle ABC are a.b.c. When the triangle ABC is an acute triangle and the triangle is an obtuse triangle, the relation between a2+b2 and c2 is... The three sides of triangle ABC are a.b.c. What is the relationship between a^2+b^2 and c^2 when the triangle ABC is an acute triangle and an obtuse triangle? Why?

Cosine theorem a^2= b^2+ c^2-2·b·c·cosA
B^2= a^2+ c^2-2·a·c·cosB
C^2= a^2+ b^2-2·a·b·cosC,
Therefore, an acute triangle a^2+b^2> c^2
Obtuse triangle a^2+b^2

In triangle abc, angle A =1/3 angle B =1/4 angle C, then is the triangle obtuse or right or acute

Cause angle A =(1/3) angle B =(1/4) angle C
That is, B=3A, C=4A
In triangular ABC, A+B+C =180 degrees
I.e. A+3A+4A=180
I.e.8A =180 degrees
A =22.5 degrees
B=3A=3*22.5=67.5 degrees
C=4A=4*22.5=90 degrees
A triangle that meets the conditions is a right triangle.

Cause angle A =(1/3) angle B =(1/4) angle C
That is, B=3A, C=4A
In triangle ABC, A+B+C =180 degrees
I.e. A+3A+4A=180
I.e.8A =180 degrees
A =22.5 degrees
B=3A=3*22.5=67.5 degrees
C=4A=4*22.5=90 degrees
A triangle that meets the conditions is a right triangle.

In △ABC, if ∠A:∠B:∠C=2:3:5, what is the triangle (" acute ""right angle "or" obtuse ")

180*5/10=90 Is right angle

P vector =(a+c, b) q vector =(b-a, c-a) if p vector is parallel to q vector then c

Coordinate operation according to vector
(A+c)(c-a)=b (b-a)
C2- a2= b2- ab
C2= a2-ab+b2
C=+/-√(a2-ab+b2)

△The lengths of the opposite sides of the three internal angles A, B and C of ABC are a, b and c respectively. Let the vector P=(a+c, b), Q=(b−a, c−a), if P∥ Q, the size of angle C is ______.

Because

P∥

Q, get
A+c
B−a=b
C−a: b2-ab=c2-a2
I.e. a2+b2-c2=ab
By cosine theorem cosC=a2+b2−c2
2Ab=1
2
So C=π
3
Therefore, the answer is:π
3