Manipulate kinematic geometric parameters, solve angle pair systems, and verify proportional trigonometric invariants in real-time.
Trigonometry Unit Ruler
Visualizing foundational trigonometric ratios on the Unit Triangle (Hypotenuse = 1.00 unit).
Kinematic Controls
Adjust Angle (θ):
Readings (Hypotenuse = 1.00)
Angle (θ): °
Base (Adjacent) Length:
0.000
Since Hypotenuse = 1, Base = cos(θ)
Perpendicular (Opposite) Length:
0.000
Since Hypotenuse = 1, Perpendicular = sin(θ)
Louisiana Standard Connection: For any right triangle with a unit hypotenuse, side lengths are uniquely determined by angle θ: Base = cos(θ) and Perp = sin(θ).
Complex Perimeter Measurement
Calculate the perimeter of rectilinear coordinate polygons via absolute values (LA Math Standard 6.G.A.3).
1. Define Vertices (x, y)
Enter coordinates (one per line, max 8 points):
2. Results
Total Perimeter: 0 units
Side Lengths:
Ensure segments share identical X or Y coordinates to strictly follow rule 6.G.A.3.
Missing Angle Calculations
Apply fundamental geometric postulates to solve for interior and supplementary angles.
Louisiana Standard Connection: Utilize supplementary facts and the triangle sum theorem (Σ = 180°) to solve unknown figures algebraically.
Angle Relationship Visualizer
Triangle Sum Theorem (Σ = 180°)
Calculated Angle C:
50°
Angles A and B must sum to strictly less than 180°.
Supplementary Angles (Σ = 180°)
Calculated Missing Angle (β):
55°
Angle Pair Algebra
Equate algebraic expressions across intersecting straight lines to solve for $x$ (7.G.B.5).
Louisiana Standard Connection (7.G.B.5): Model vertical and linear pair relationships as linear equations ($Ax + B = Cx + D$).
Visualizer
Vertical Angles (Angle 1 = Angle 2)
Calculated $x$ Value:
$x =$ 30.00
Evaluated Measure:
75.00°
Supplementary Angles (Σ = 180°)
Calculated $x$ Value:
$x =$ 27.00
A1: 118.00°
A2: 62.00°
Proportional Side Ratios (Pre-Trig)
Demonstrate that triangle side ratios remain invariant across uniform dilations.
Base T1
Adj ($b_1$): 100.00
Opp ($a_1$): 100.00
Hyp ($c_1$): 141.42
Ratio A/B: 1.000
Scaled T2
Adj ($b_2$): 150.00
Opp ($a_2$): 150.00
Hyp ($c_2$): 212.13
Ratio A/B: 1.000
Invariance Postulate: Because the acute angle θ is held constant, the ratio $\frac{\text{Opposite}}{\text{Adjacent}}$ remains unchanged, directly establishing the trigonometric tangent definition.
Unknown Lengths via Scaling
Calculate unknown dimensional vectors across similar figures using scale factor $k$ (7.G.A.1).
Dimensional Parameters
Rectangle A
Rectangle B
Scale Factor ($k$):
1.50
Unknown Width ($W_B$):
60.00
Pythagorean Theorem Geometry
Verify area summation geometrically: $\text{Area}_A + \text{Area}_B = \text{Area}_C$ (8.G.B.7).
Solve Unknown Leg or Hypotenuse
$3^2 + 4^2 = c^2$
Solved Side Dimension:
5.00
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Distance in the Coordinate Plane
Interactive planar metric $d = \sqrt{(\Delta x)^2 + (\Delta y)^2}$ (8.G.B.8). Drag handles on the canvas.
Point Registers
Point P1
$x_1$: 0.00
$y_1$: 0.00
Point P2
$x_2$: 0.00
$y_2$: 0.00
$\Delta x = x_2 - x_1$: 0.00
$\Delta y = y_2 - y_1$: 0.00
$d^2 = \Delta x^2 + \Delta y^2$: 0.00
Resolved Distance ($d$):0.00
Converse of the Pythagorean Theorem
Compare $a^2 + b^2$ against $c^2$ to classify acute, right, and obtuse triangles.
Input Side Lengths ($a, b, c$)
Sum of Squares ($a^2 + b^2$): 25.00
Longest Squared ($c^2$): 25.00
Classification:Right Triangle
Trigonometric Ratios (SOH CAH TOA)
Demonstrating that right triangle ratios depend solely on angle θ, invariant of triangle scale (G-SRT.C.6).