Pythagorean Theorem & Trigonometry (Angles & Sides) Solver

Pythagorean Theorem + Trigonometry (angles & sides) Solver

This interactive calculator uses the Pythagorean theorem \( H^2 = S_1^2 + S_2^2 \) and standard trigonometric ratios (sine, cosine, tangent) to solve right triangles. Choose the calculation mode, enter any two values — decimal values allowed — and get the remaining sides and angles instantly.

Right triangle with sides S1, S2 and hypotenuse H. Angles: A opposite S2, B opposite S1, C = 90°

Pythagorean theorem & fundamental formulas

Pythagorean: \( H^2 = S_1^2 + S_2^2 \) | Trigonometry: \( \sin(A) = \dfrac{S_2}{H}, \quad \sin(B) = \dfrac{S_1}{H}, \quad \cos(A) = \dfrac{S_1}{H}, \quad \tan(A) = \dfrac{S_2}{S_1} \)

Where: angle C = 90° (right angle).

Interactive solver — choose mode

Select what you know: two sides, hypotenuse+side, or hypotenuse+angle.

Calculation mode:

📐 Mode 1: Two sides (S₁ , S₂)

Side S₁ :

Side S₂ :

📐 Mode 2: Hypotenuse + side S₁

Hypotenuse H :

Side S₁ :

Enter H and S₁. The missing side S₂ and angles will be computed.

📐 Mode 3: Side S₁ + angle A

Side S₁ :

Angle A (degrees) :

Angle A must be acute (<90°). The sides S₂, H and angle B will be computed.

📐 Mode 4: Hypotenuse + angle B

Hypotenuse H :

Angle B (degrees) :

Angle B is acute (<90°). The sides S₁, S₂ and angle A will be computed.

Decimal places:

Results

Side S₁ —

Side S₂ —

Hypotenuse H —

Angle A —°

Angle B —°

Angle C 90°

Step‑by‑Step Solution

Click "Calculate" to see the detailed steps.

Why use this all‑in‑one calculator?

Four clear modes – Two sides, hypotenuse+side S₁, side S₁+angle A, hypotenuse+angle B.

Accurate & instant – Uses both theorem and trigonometric functions (sin, cos, tan).

Angle‑aware – Automatically computes angles A and B in degrees.

Decimal friendly – Input any positive real numbers; choose output precision.

Learning oriented – Shows detailed step‑by‑step solution below.

Pythagorean Theorem + Trigonometry (angles & sides) Solver

Pythagorean theorem & fundamental formulas

Interactive solver — choose mode

Step‑by‑Step Solution

Why use this all‑in‑one calculator?

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