Question

A triangle has side lengths of 12 cm, 5 cm, and 9 cm. Classify it as acute, obtuse, or right.

Answer 1

Answer:

• Obtuse

Step-by-step explanation:

Use Pythagorean to determine the type of the triangle.

If the square of the longest side is equal to sum of the squares of the other sides, it is right, if smaller, then the triangle is acute, if greater, then the triangle is obtuse.

• 5² + 9² ? 12²
• 25 + 81 ? 144
• 106 < 144

This shows the angle opposite to the longest side is greater than 90°

Hence the triangle is obtuse

Answer 2

Obtuse

Angle ∠ A = α = 114.975° = 114°58'30″ = 2.007 rad

Angle ∠ B = β = 22.192° = 22°11'30″ = 0.387 rad

Angle ∠ C = γ = 42.833° = 42°50' = 0.748 rad