How does the Triangle Calculator solve right-angled triangles?

The calculator applies the Pythagorean theorem (a² + b² = c²) to compute the hypotenuse and uses inverse trigonometric functions (arctan) to find unknown acute angles.

What is Heron's formula for triangle area?

Heron's formula calculates triangle area from the lengths of all three sides: Area = sqrt(s*(s-a)*(s-b)*(s-c)), where s = (a+b+c)/2 is the semi-perimeter.

Can this calculator solve SSS, SAS, and ASA triangles?

Yes. You can solve triangles given three sides (SSS using Law of Cosines), two sides and an included angle (SAS), or two angles and a side (ASA using Law of Sines).

What trigonometric ratios are calculated?

The calculator computes sine, cosine, and tangent ratios for angle A automatically.

Geometry & Trigonometry Solver

Triangle Calculator – Sides, Angles, Area & Hypotenuse

Solve any triangle using Right Triangle (Pythagorean theorem), SSS (3 sides), SAS, or ASA theorems. Compute hypotenuse, angles, area, perimeter, and sin/cos/tan ratios.

Triangle Area -

Calculated Triangle Area

Leg a (Opposite)

Leg b (Adjacent)

Side a

Side b

Side c

Side a

Included Angle C (°)

Side b

Angle A (°)

Included Side c

Angle B (°)

Geometry Visualization Right Scalene

Triangle Area-

Perimeter

Hypotenuse c

Angle A

Angle B

Trig Ratios

Triangle Geometry & Trigonometry Guide

Triangles are fundamental geometric polygons governed by precise trigonometric laws. Whether solving right triangles in construction or calculating non-right oblique triangles in surveying, understanding geometric relationships ensures accurate dimensions.

Core Theorems:

Pythagorean Theorem: $c^2 = a^2 + b^2$ for right triangles.
Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$ for SSS and SAS configurations.
Law of Sines: $\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$ for ASA and AAS triangles.
Heron's Formula: $\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$ where $s = \frac{a+b+c}{2}$.

How do you find the hypotenuse of a right triangle?

Square both legs (a and b), add them together, and take the square root: $c = \sqrt{a^2 + b^2}$.

What is Heron's formula used for?

Heron's formula calculates the exact area of any triangle when you know all three side lengths without needing the height.

How are angles computed from side lengths?

For right triangles, acute angles are derived using $\arctan(\frac{a}{b})$. For general triangles, the Law of Cosines is used.

What is the triangle inequality theorem?

The sum of the lengths of any two sides of a triangle must always be strictly greater than the length of the remaining side ($a + b > c$).