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Pythagorean Theorem Calculator – Find Hypotenuse & Triangle Sides | Solvezi
Pythagorean Theorem Calculator – Find Hypotenuse & Triangle Sides | Solvezi
Solve any right triangle using geometry and trigonometry (SOH CAH TOA)
Geometric Centers
Side a = 3.0000 units
Side b = 4.0000 units
Angle C = 90°
Formula: c = √(a² + b²)
c = √( (3.0000)² + (4.0000)² )
c = √(25.0000)
c = 5.0000 units
Formula: tan(A) = a ÷ b
A = arctan(3.0000 ÷ 4.0000)
A = 36.8699°
Formula: B = 90° − A
B = 53.1301°
Area = (a × b) ÷ 2 = (3.0000 × 4.0000) ÷ 2 = 6.0000 sq. units
Perimeter = a + b + c = 3.0000 + 4.0000 + 5.0000 = 12.0000 units
Inradius (r) = (a + b − c) ÷ 2 = 1.0000 units
Circumradius (R) = c ÷ 2 = 2.5000 units
Check: a² + b² = c²
9.0000 + 16.0000 = 25.0000
25.0000 ≈ 25.0000 ✓
This section provides a quick breakdown of the core mathematical principles used to solve right triangles. All calculations rely on the Pythagorean Theorem and fundamental Trigonometric Ratios (SOH CAH TOA).
Relates the two legs (a and b) to the hypotenuse (c).
Relate acute angles (A, B) to side ratios (SOH CAH TOA).
The two acute angles are complementary.
The height from the right angle (C) perpendicular to the hypotenuse (c).
| Mode | Values Entered | Primary Formulas Used |
|---|---|---|
| Two Sides (a, b) | a, b | c = √(a² + b²) | tan(A) = a / b | B = 90° - A |
| Side a + Hypotenuse | a, c | b = √(c² - a²) | sin(A) = a / c | B = 90° - A |
| Side a + Angle A | a, A | B = 90° - A | b = a / tan(A) | c = a / sin(A) |
| Hypotenuse + Angle A | c, A | B = 90° - A | a = c × sin(A) | b = c × cos(A) |