Figure

Shapes and geometry

Oblique triangles

Find angles and area from three measured sides with the Law of Cosines.1

A measured triangle does not need a right angle. Keep each side paired with its opposite angle: a with A, b with B, and c with C. Three valid side lengths determine the angles and area.

Angles A, B and C

Match a, b and c to your sketch. Each angle faces its matching side.

Start a new calculation

Use 2nd if a unit is above its button.

  1. Start fresh

    Press Clear entry, then Clear entry.

  2. Press the keys

    Press Select length units.

Assign the sides

Measured triangle: side a faces angle A, side b faces angle B, and side c faces angle C. Preserve these assignments when storing measurements.abcABC
Schematic, not to scale.

1. Open Oblique

Skip Close if no mode is open.

  1. Press Close calculation mode, then Open Oblique Triangle.

2. Enter side a

  1. Side a

    Press 38, then feet, then 5, then inches, then Store side a.

Enter side b

  1. Side b

    Press 23, then feet, then 4, then inches, then 9, then Fraction, then 16, then Store side b.

Enter side c

  1. Side c

    Press 26, then feet, then 1, then inches, then 13, then Fraction, then 16, then Store side c.

3. Find angle A

  1. Press Equals.

Results in orderPress = to continue

  1. Angle A101.5734°
  2. Angle B36.59978°
  3. Angle C41.8268°
  4. Triangle area299.4929 square feet
  5. Stored a38 feet 5 inches
  6. Stored b23 feet 4 and 9/16 inches
  7. Stored c26 feet 1 and 13/16 inches
  8. Angle A again101.5734°

Keep in mind

Each angle faces its matching side. = cycles the angles, area and entered sides. To correct a side, enter its replacement and press a, b or c. Tap Close in the top rail to return to the regular keys. Your sides stay available until you clear the calculation.

Display assumptions

  1. Fraction precision: 1/16″; Fraction format: Simplified; Angle decimal places: Variable; Area units: Automatic. ↩

Keep the guide beside your calculation.

These examples are built into Figure. Open Help while you calculate, then return to the same guide and reading position.

See Help in Figure →