Solve any maths problem

Equations, derivatives, integrals, matrices, triangles, primes, statistics — or a word problem the tutor breaks into parts.

Geometry · Triangles

Triangle 3 4 5

3,\ 4,\ 5

Step by step

  1. a = 3,\ b = 4,\ c = 5

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

  2. P = a + b + c = 12

    Perimeter.

  3. s = \tfrac{P}{2} = 6,\quad A = \sqrt{s(s-a)(s-b)(s-c)} = 6

    Heron's formula for the area.

  4. \cos A = \frac{b^2 + c^2 - a^2}{2bc} = \frac{4}{5} \Rightarrow A \approx 36.870^\circ

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

  5. \cos B = \frac{a^2 + c^2 - b^2}{2ac} = \frac{3}{5} \Rightarrow B \approx 53.130^\circ

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

  6. \cos C = \frac{a^2 + b^2 - c^2}{2ab} = 0 \Rightarrow C \approx 90.000^\circ

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

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

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

Reveal the answer
A = 6,\quad P = 12,\quad \angle \approx 36.9^\circ, 53.1^\circ, 90.0^\circ