Question

1. name the triangle with the following characteristics. sides: 2 cm, 3 cm, 4 cm; angle: 29°.

○ right isosceles triangle
○ acute scalene triangle
○ obtuse scalene triangle
○ right scalene triangle

Explanation:

Step1: Analyze side lengths

Check if sides are equal. Sides: 2 cm, 3 cm, 4 cm (all different), so scalene.

Step2: Analyze angle type

One angle is \(29^\circ\) (acute). Check largest angle using Law of Cosines: \(c^2 = a^2 + b^2 - 2ab\cos C\). For \(c = 4\), \(a = 2\), \(b = 3\): \(16 = 4 + 9 - 12\cos C\) → \(12\cos C = -3\) → \(\cos C = -0.25\), so \(C \approx 104.48^\circ\) (obtuse).

Step3: Classify triangle

Scalene (all sides different) and obtuse (one angle > \(90^\circ\)) → obtuse scalene triangle.

Answer:

obtuse scalene triangle (matching the option: obtuse scalene triangle)