What are the angles and area of a triangle with sides of 2.60cm by 2.85cm by 4.70cm?

Answer 1

Let angle A be opposite side a and between sides b and c; using the cosine rule you can find each angle:

a² = b² + c² - 2bc cos A

→ A = arc cos((b² + c² - a²)/2bc)

→ Angles are:

1. arc cos((2.85² + 4.7² - 2.6²)/(2 × 2.85 × 4.7)) ≈ 28.9°
2. arc cos((2.6² + 4.7² - 2.85²)/(2 × 2.6 × 4.7)) ≈ 32.0°
3. arc cos((2.6² + 2.85² - 4.7²)/(2 × 2.6 × 2.85)) ≈ 119.1°

Note that the third angle can also be worked out form 180° - (28.9° + 32.0°) = 180° - 60.1° = 119.1°

Area triangle = ½bc sin A ≈ ½ × 2.85 × 4.7 × sin(28.9°) ≈ 3.24 cm²

Answer 2

They are 28.9, 32.0, and 119.1 degrees.