Class 10 · Chapter 8 · Interactive Lab
Imagine sighting the top of the Qutub Minar, or a girl on a balcony spotting a flower pot across a river — every one of those is a right triangle waiting to be measured. Drag the sighting line below to build the triangle yourself; the ratios update live.
Drag the coral sighting point C around the arc to change ∠A. B is the foot of the perpendicular, so ABC is always right-angled at B. Watch opposite, adjacent and hypotenuse relabel themselves, and all six ratios update from the actual side lengths.
● C is draggable along the arc · A is the angle · B is the right angle
Three similar right triangles, same angle A, different sizes — exactly like triangles PAM, CAB and QAN in the textbook figure. Change the angle and watch every triangle grow or shrink together, while sin A, cos A and tan A stay identical for all three.
small · medium · large — all share angle A
Snap to a standard angle and see the exact construction the textbook uses: the isosceles right triangle for 45°, and the bisected equilateral triangle for 30° / 60°. The matching column lights up in Table 8.1.
pick an angle below to rebuild the construction
| ∠A | 0° | 30° | 45° | 60° | 90° |
|---|
All three identities come from Pythagoras' theorem on the same right triangle. Slide the angle anywhere in its valid range and watch each identity hold exactly, no matter what A is.
sin²A + cos²A = 1 · 1 + tan²A = sec²A · 1 + cot²A = cosec²A
right triangle used to derive all three identities