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# CALC 1 Triangles Calculator

This calculator will calculate the solution of plane triangles.

From the Wikipedia reference, Solution of triangles:

A general form triangle has six main characteristics (see picture): three linear (side lengths abc) and three angular (αβγ). The classical plane trigonometry problem is to specify three of the six characteristics and determine the other three.
For all cases in the plane, at least one of the side lengths must be specified.  ## Triangle Calculation Example 1, SSS

Value Keystrokes Display Description
shift C tri 0 Clears the triangle values
3 side a 3.00 Stores the length of side a
4 side b 4.00 Stores the length of side b
5 side c 5.00 Stores the length of side c
d 5.00 Calculates the diameter of the triangle circumcircle.

To calculate the remaining characteristics, the area, d, or any of the 6 characteristic keys can be pressed.

The History item will have the values shown on the keys:

Calculates the diameter of the triangle's circumcircle.
3.000 : Side a.
4.000 : Side b.
5.000 : Side c.
36.87 : Angle α.
53.13 : Angle β.
90.00 : Angle γ.
6.000 : The area.
5.000 : The diameter of the triangle's circumcircle.

## Triangle Calculation Example 2, Two angles and one side.

Value Keystrokes Display Description
shift C tri 0 Clears the triangle values
10 side b 10.00 Stores the length of side b
85 ∠ α 85.0 Stores angle α
65 ∠ γ 65.0 Stores angle γ
side a 19.92 Calculates the remaining characteristics and the area and returns side a.

The History item will have the values shown on the keys:

Calculates the area of the triangle.
19.92 : Side a.
10.00 : Side b.
18.13 : Side c.
85.00 : Angle α.
30.00 : Angle β.
65.00 : Angle γ.
90.29 : The area.

## Triangle Calculation Example 3, One angle and two sides, unique solution.

Value Keystrokes Display Description
shift C tri 0 Clears the triangle values
10 side a 10.00 Stores the length of side a
7 side c 7.00 Stores the length of side c
30 ∠ α 30 Stores angle γ
area 27.00 Calculates the remaining characteristics and the area.

The History item will have the values shown on the keys:

Calculates the area of the triangle.
10.00 : Side a.
15.43 : Side b.
7.000 : Side c.
30.00 : Angle α.
129.5 : Angle β.
20.49 : Angle γ.
27.00 : The area.

## Triangle Calculation Example 4, One angle and two sides, two solutions.

Value Keystrokes Display Description
shift C tri 0 Clears the triangle values
7 side a 7.00 Stores the length of side a
10 side c 10.00 Stores the length of side c
30 ∠ α 30 Stores angle γ
d 14.0 Calculates the remaining characteristics and the diameter of the triangle's circumcircle.

There will be a "* 2 Solutions *" message at the top of the display in the status label.

The History item will have the values shown on the keys and more information if you wish to find the other solution:

Calculates the diameter of the triangle's circumcircle.
Another solution exists if angle 45.58
is set to 180 - 45.58 = 134.4
7.000 : Side a.
13.56 : Side b.
10.00 : Side c.
30.00 : Angle α.
104.4 : Angle β.
45.58 : Angle γ.
33.90 : The area.
14.00 : The diameter of the triangle's circumcircle.

See the Wikipedia reference, Two sides and non-included angle given (SSA), 3.2 for details.

To solve for the second solution:

Value Keystrokes Display Description
180-RCL ∠ γ = 134.4 Calculates the obtuse value.
STO ∠ γ 134.4 Stores angle γ.
0 ∠ β 0 Zeros the angle so it will be recalculated.
0 side b 0 Zeros the side so it will be recalculated.
area 9.403 Calculates the remaining characteristics and the area.

The History item will have the values shown on the keys:

Calculates the area of the triangle.
7.000 : Side a.
3.761 : Side b.
10.00 : Side c.
30.00 : Angle α.
15.58 : Angle β.
134.4 : Angle γ.
9.403 : The area.

## Triangle Calculation Example 5, Rectangular coordinates.

Vertex A = 0,0
Vertex B = 2,0
Vertex C = 4,3

Value Keystrokes Display Description
shift C tri 0 Clears the triangle values
3, = 4 →P 5 Calculates side b and angle α
5 STO side b 5 Stores side b
5 SWAP, STO ∠ α 36.9 Stores angle α
2 STO side c 2.0 Stores side c
area 3.00 Calculates the remaining characteristics and the area.

The History item will have the values shown on the keys:

Calculates the area of the triangle.
3.606 : Side a.
5.000 : Side b.
2.000 : Side c.
36.87 : Angle α.
123.7 : Angle β.
19.44 : Angle γ.
3.000 : The area.

## If More Than Three Characteristics Are Entered

A zero value indicates an unknown characteristic to be calculated. All values must be >= 0.

1. If 3 sides are entered, they will be used and any angles entered will be recalculated.
2. If 3 angles are entered, angle γ will be recalculated.
3. If 2 sides and 2 angles are entered, the 2 angles will be used to calculate the 3rd angle. Then the 1st side entered (>0. a, b, c respectively) will be used to calculate the remaining sides.

## Using the "STO/RCL tri" Keys

Tapping STO + "tri 1" (2,3,4) will store all 6 of the current characteristics.

Tapping RCL + "tri 1" (2,3,4) will recall all 6 of the stored characteristics.

## Other Keys

See Rectangular to Polar Keys for using the "→P" and "→R" keys.

These keys are useful to for converting rectangular coordinates to the polar lengths and angles for triangle solutions. See example 5.

The →H.fp, and →HMS keys can be used to convert degree, minute, second values to Deg.fp and back.