Right Triangle Calculator

Right Triangle is evaluated from Leg a, Leg b and Hypotenuse c. The calculation reports Leg a, Leg b and Hypotenuse c.

Results

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About the Right Triangle Calculator

Right Triangle is treated here as a quantitative relation between Leg a, Leg b, Hypotenuse c and Angle A and Leg a, Leg b, Hypotenuse c and Angle A.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
a^2 + b^2 = c^2 (Pythagorean theorem)
sin(A) = a/c, cos(A) = b/c, tan(A) = a/b
Angle B = 90 deg - A

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

a^2 + b^2 = c^2 (Pythagorean theorem)
sin(A) = a/c, cos(A) = b/c, tan(A) = a/b
Angle B = 90 deg - A

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Roof Rafter Length — 6/12 Pitch

Inputs

leg_a: 14 leg_b: 28
Leg a: 14. Leg b: 28. Hypotenuse c: 31.304952. Angle A: 26.5651 deg. Angle B: 63.4349 deg. Area: 196 units^2. Perimeter: 73.305 units. sin: 0.447214. cos: 0.894427. tan: 0.5

With Leg a = 14 and Leg b = 28 as the stated inputs, the result is Leg a = 14, Leg b = 28 and Hypotenuse c = 31.304952. Each value corresponds to the declared output fields.

Example 2: Staircase Rise and Run

Inputs

hypotenuse: 12 angle_A: 35
Leg a: 6.882917. Leg b: 9.829825. Hypotenuse c: 12. Angle A: 35 deg. Angle B: 55 deg. Area: 33.8289 units^2. Perimeter: 28.7127 units. sin: 0.573576. cos: 0.819152. tan: 0.700208

With Hypotenuse c = 12 and Angle A = 35 as the stated inputs, the result is Leg a = 6.882917, Leg b = 9.829825 and Hypotenuse c = 12. Each value corresponds to the declared output fields.

Example 3: 30-60-90 Triangle — Special Angles

Inputs

hypotenuse: 10 angle_A: 30
Leg a: 5. Leg b: 8.660254. Hypotenuse c: 10. Angle A: 30 deg. Angle B: 60 deg. Area: 21.6506 units^2. Perimeter: 23.6603 units. sin: 0.5. cos: 0.866025. tan: 0.57735

With Hypotenuse c = 10 and Angle A = 30 as the stated inputs, the result is Leg a = 5, Leg b = 8.660254 and Hypotenuse c = 10. Each value corresponds to the declared output fields.

Example 4: 3-4-5 Pythagorean Triple — Foundation Layout

Inputs

leg_a: 6 leg_b: 8
Leg a: 6. Leg b: 8. Hypotenuse c: 10. Angle A: 36.8699 deg. Angle B: 53.1301 deg. Area: 24 units^2. Perimeter: 24 units. sin: 0.6. cos: 0.8. tan: 0.75

With Leg a = 6 and Leg b = 8 as the stated inputs, the result is Leg a = 6, Leg b = 8 and Hypotenuse c = 10. Each value corresponds to the declared output fields.

Common Use Cases

  • Find hypotenuse from two legs
  • Find leg from hypotenuse and one angle
  • Calculate roof rafter length
  • Determine staircase rise and run