In ΔABC, right-angled at B, AB = 20 cm and BC = 21 cm. Find all six trigonometric ratios of angle A and of angle C.

1. 1 · Write what is given and what is to be found Given: ΔABC, ∠B = 90°, AB = 20 cm, BC = 21 cm. To find: the six ratios of ∠A and ∠C.
2. 2 · Draw the figure Right triangle with the right angle at B. Mark ∠A and ∠C. Write 20 cm on AB and 21 cm on BC.
3. 3 · Write the formula or theorem Pythagoras theorem: AC² = AB² + BC². sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.
4. 4 · Find the hypotenuse AC² = 400 + 441 = 841, so AC = 29 cm.
5. 5 · Write the ratios of angle A
   • sin A = 21/29, cos A = 20/29, tan A = 21/20
   • cosec A = 29/21, sec A = 29/20, cot A = 20/21
6. 6 · Write the ratios of angle C
   • sin C = 20/29, cos C = 21/29, tan C = 20/21
   • cosec C = 29/20, sec C = 29/21, cot C = 21/20
7. 7 · Check and box the answer Check: sin²A + cos²A = (441 + 400)/841 = 1. Box both sets of ratios.

Scoring tip: Name the opposite and adjacent sides for each angle before you write any ratio. They swap when you move from angle A to angle C.