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Geometry · Triangles

Triangle 2 3 4

2,\ 3,\ 4

Paso a paso

  1. a = 2,\ b = 3,\ c = 4

    Three sides (SSS). Check the triangle inequality: each side is less than the sum of the other two. ✓

  2. P = a + b + c = 9

    Perimeter.

  3. s = \tfrac{P}{2} = \frac{9}{2},\quad A = \sqrt{s(s-a)(s-b)(s-c)} = \frac{3 \sqrt{15}}{4} \approx 2.9047

    Heron's formula for the area.

  4. \cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{7}{8} \Rightarrow A \approx 28.955^\circ

    Law of cosines for angle A (opposite side a).

  5. \cos B = \frac{a^2 + c^2 - b^2}{2ac} = \frac{11}{16} \Rightarrow B \approx 46.567^\circ

    Law of cosines for angle B (opposite side b).

  6. \cos C = \frac{a^2 + b^2 - c^2}{2ab} = - \frac{1}{4} \Rightarrow C \approx 104.48^\circ

    Law of cosines for angle C (opposite side c).

  7. A + B + C = 180.0^\circ

    The angles add to 180° — a obtuse, scalene triangle.

Revelar la respuesta
A = \frac{3 \sqrt{15}}{4} \approx 2.9047,\quad P = 9,\quad \angle \approx 29.0^\circ, 46.6^\circ, 104.5^\circ