Right Angle

A right-angled triangle drawn to scale appears, with angle α marked sometimes at the bottom and sometimes at the top. For that angle, the hypotenuse is the long side, opposite the right angle; the opposite side faces α; and the adjacent side touches α without being the hypotenuse. If α moves to the other corner, opposite and adjacent swap.

Sine = opposite ÷ hypotenuse; cosine = adjacent ÷ hypotenuse; tangent = opposite ÷ adjacent. To find a side, pick the ratio that links the side you have with the one you want; for an angle, use the inverse ratio on the calculator (sin⁻¹, cos⁻¹, tan⁻¹).

There are no options: you build the ratio by tapping the top and bottom sides of the fraction, tap each side to name it, fill in the 30°, 45° and 60° table or type the result. When you answer, each side is coloured with its name relative to α: hypotenuse in yellow, opposite in pink and adjacent in blue. In the word problems (a ladder, a shadow, a kite) the triangle only appears when you answer: drawing it is part of the exercise.

⏱️ 90s · Correct +10 and +6s · Wrong −5s