Question

The sides of a triangle are m, n and
m2 +n2 + mn. What is the sum of
the acute angles of the triangle?​

Answer 1

Solution:

Solution:Concept:

Solution:Concept:Cosine rule:

Solution:Concept:Cosine rule:Where a, b and c are the sides of the triangle and θ is the angle between the sides a and b.

Solution:Concept:Cosine rule:Where a, b and c are the sides of the triangle and θ is the angle between the sides a and b.Calculation:

Solution:Concept:Cosine rule:Where a, b and c are the sides of the triangle and θ is the angle between the sides a and b.Calculation:Let m = n = 1 unit

Solution:Concept:Cosine rule:Where a, b and c are the sides of the triangle and θ is the angle between the sides a and b.Calculation:Let m = n = 1 unitThen unit

Solution:Concept:Cosine rule:Where a, b and c are the sides of the triangle and θ is the angle between the sides a and b.Calculation:Let m = n = 1 unitThen unitUsing cosine rule;

Solution:Concept:Cosine rule:Where a, b and c are the sides of the triangle and θ is the angle between the sides a and b.Calculation:Let m = n = 1 unitThen unitUsing cosine rule;⇒ cos θ = -1/2

Solution:Concept:Cosine rule:Where a, b and c are the sides of the triangle and θ is the angle between the sides a and b.Calculation:Let m = n = 1 unitThen unitUsing cosine rule;⇒ cos θ = -1/2∴ θ = 120°

Solution:Concept:Cosine rule:Where a, b and c are the sides of the triangle and θ is the angle between the sides a and b.Calculation:Let m = n = 1 unitThen unitUsing cosine rule;⇒ cos θ = -1/2∴ θ = 120° Now, the sum of the acute angles of the triangle = 180° - 120° = 60