Skill: trig-ratios
Trig Ratios Practice
An endless supply of never-repeating trig-ratio problems with instant feedback. Find sines, cosines, and tangents,
solve for sides with special angles, find angles with inverse trig, and work the ladder and shadow problems where SOHCAHTOA earns its keep.
1 Practice
Type your answer and press Check answer (or Enter). A wrong answer earns a hint first;
a second miss walks you through the full solution.
How to enter answers
- Ratios:
5/13as a fraction — or a decimal like0.3846(within ±0.01). - Radical answers: type
sqrt48,√48, or4sqrt3for exact form —
or type a decimal like6.93. Both are accepted. - Angles: type the degrees like
61.93(the°sign is optional) — accepted within ±0.05°.
2 What you’ll practice
Every problem is generated fresh from 12 templates — a problem never repeats until its whole pool is used up.
SOHCAHTOA ratios
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
Type the fraction or a decimal.
Sides from special angles
Use the exact values at 30°, 45°, 60°. Type sqrt48, 4sqrt3,
or a decimal.
Angles & word problems
Undo a ratio with inverse trig (θ = sin¹(ratio)), and solve ladder
and shadow stories.
3 Watch out for these
The three mistakes students make most often on Pythagoras problems.
Wrong: using the side next to θ as “opposite” in sine.
Right: opposite is across from θ. Label all three sides before choosing a ratio.
Wrong: sin(30) = −0.988, then building a whole word problem on it.
Right: sin 30° = 0.5 — look for the “D” (degree) indicator first.
Wrong: sin θ = 0.6 → “θ = 0.6.”
Right: θ = sin¹(0.6) ≈ 36.87°. A ratio is not an angle.