A triangle-solving practice app. Each problem gives
you some known information about a right triangle and asks you to find
the remaining sides and/or angles. The right angle is always at vertex
C (blue).
🎛️ How to Use
- Choose a triangle type (and optionally toggle Enable SohCahToa), then press New Problem.
-
The canvas shows the triangle with known values labeled in
green and unknown
sides or angles shown as ?.
Known angles are shown in purple.
-
Type your answers in the Find: fields.
For radical answers, use the √ button to
insert the radical symbol, then type the radicand.
Examples: 3√5 √2
4√3
For SohCahToa side problems, enter decimal answers
rounded to 2 decimal places (e.g. 8.45).
For angle answers enter decimal degrees (e.g. 36.87).
- Press ✓ Check to see which answers are correct.
-
Stuck? Expand 💡 Show hint for a reminder
of the relevant ratio or theorem, or press
👁 Reveal to see the full answers.
△ Triangle Types
The right angle is always at
C.
Sides: a = BC (vertical leg, opp ∠A),
b = CA (horizontal leg, opp ∠B),
c = AB (hypotenuse).
| Type |
Angles |
Side values |
Given → Find |
| 30-60-90 |
30°, 60°, 90° |
s,
s√3,
2s
|
1 side → 2 sides (exact) |
| 45-45-90 |
45°, 45°, 90° |
s, s,
s√2
|
1 side → 2 sides (exact) |
| Right (Pythagorean) |
90°, ∠A, ∠B |
a, b, c (all integers) |
2 legs → hyp + 2 angles |
| General Right ▵ |
90°, ∠A, ∠B |
Integer and/or radical sides (e.g. √5, 2√3) |
1–2 sides → remaining sides (exact radical form).
When SohCahToa is on, also mixes in trig problems (see below).
|
| SohCahToa ▵ toggle |
90°, ∠A (known integer), ∠B (?) |
One integer side given; others are decimal |
Side-finding: 1 side + ∠A → 2 decimal sides + ∠B.
Angle-finding: 2 integer sides → ∠A (decimal degrees).
|
🧮 SohCahToa Toggle
-
The Enable SohCahToa switch (on by default) adds
trigonometry problems to the pool when Random is selected,
and mixes them 50/50 into General Right ▵ problems.
-
Side-finding problems give you one integer side and
∠A. Apply SOH, CAH, or TOA to find both unknown sides
(rounded to 2 decimal places), then use ∠B = 90° − ∠A.
-
Angle-finding problems give you two sides from a
Pythagorean triple. Use the appropriate inverse trig function
(sin−1, cos−1, or tan−1)
to find ∠A (rounded to 2 decimal places).
-
Turn the toggle off to restrict practice to
non-trig problems only.
-
New to sine, cosine, and tangent?
Understanding SohCahToa
covers the history, the ratios, inverse trig, and includes an
interactive calculator.
√ Entering Answers
- Radical (coefficient × √)
-
Type the coefficient, then press √,
then type the radicand. Example: for
3√5
type
3√5. Leave the coefficient blank for
√2 (= 1 × √2).
- Decimal sides (SohCahToa)
-
Type the value rounded to 2 decimal places, e.g.
8.45.
The √ button is hidden for these inputs since exact radical
form is not required.
Accepted within ±0.02 units.
- Angles
-
Enter in decimal degrees (e.g.
36.87).
Complementary angles like ∠B for a SohCahToa side problem
will be a whole number (e.g. 55).
Accepted within ±0.15°.
- Simplification
-
Radical answers must be in simplified form
(e.g.
2√3, not √12).
If your answer is unsimplified, the field turns orange and you
are prompted to simplify. The simplified form is revealed after
3 failed attempts.
🧑💻 Developer Notes
- Developer
- klp + GitHub Copilot
- Date
- May 2026
- Stack
- SketchWaveJS · p5.js 1.6.0 · Bootstrap 5.3.2
- Key files
-
solvTri1Sketch.js — problem generation, canvas
drawing, answer checking.
resources/Radical.js — radical-expression class
for exact-form side values.
DecimalVal (inline class) — duck-typed Radical
replacement for SohCahToa decimal sides.