A 9 m ladder leans against a wall and makes 60° with the ground. Find how high up the wall it reaches and how far its foot is from the wall. (Use √3 = 1.732)

1. 1 · Write what is given and what is to be found Given: ladder AC = 9 m, ∠ACB = 60°, wall AB vertical. To find: AB and BC.
2. 2 · Draw the figure Vertical wall AB, ground BC, ladder AC. Right angle at B, 60° at C.
3. 3 · Write the formula or theorem sin 60° = AB/AC and cos 60° = BC/AC.
4. 4 · Find the height √3/2 = AB/9, so AB = 9√3/2 = 4.5 × 1.732 = 7.794 ≈ 7.79 m.
5. 5 · Find the distance 1/2 = BC/9, so BC = 4.5 m.
6. 6 · Check and box the answer The ladder reaches about 7.79 m up the wall and its foot is 4.5 m away. Check: 7.794² + 4.5² ≈ 60.75 + 20.25 = 81 = 9².

Scoring tip: The ladder is the hypotenuse, so use sin for the height and cos for the distance. Using tan here needs an extra step and wastes time.